Tools

Component Properties
PPM per °C PPM Temperature Coefficient Capacitor Code ↔ Value Zener Diode Zener Diode Shunt Reg. Resistor Colour ↔ Value Resistor Colour to value LED Resistor
Device Properties
Multimeter Uncertainty
Passive Circuits
RC Charge/Discharge LC Resonant Frequency RLC Impedance ser. RLC Impedance ser./par. Reactance (Xc, Xl) I Reactance (Xc, Xl) II Q Factor Parallel Resistors Voltage Divider RC Filter 1st Order RC Filter 1st Order II RC Filter 1st-4th Order
Power, Energy & Regulators
Power Dissipation DC PSU Efficiency Battery Life Estimator Joule ↔ Watt-hour Energy in a Capacitor Energy in an Inductor Rectifier Ripple PSU Ripple (with DC) Volt Drop wire/cable SMPS Duty & Ripple V.Reg Cap. Designer LM317 Regulator LM337 Regulator
Amplifiers
Op-Amp (inverting) Op-Amp (inverting) II Op-Amp (non-inverting) Op-Amp (non-inverting) II
Frequency, Timing & Waves
Time / Frequency 555 Timer 555 Timer II Duty Cycle ↔ On/Off T. Wavelength ↔ Freq. Quarter-Wave Resonator Transmission Line Z₀
Measurement & Conversion
dB Conversions dBm ↔ mW / W Signal-to-Noise Ratio Decimal ↔ Scientific SI Units ↔ Scientific mm ↔ mils Rectangular ↔ Polar LED Matrix Font Gen.
Material & Field Effects
Current Density Skin Depth Wire Resistance
Fundemental Laws
Ohm’s Law (V=IR) Joule’s Law (P=I²R) Kirchhoff's Law (KCL + KVL) Lenz’s Law Faraday’s Law Coulomb’s Law Gauss’s Law Ampère's Law Biot-Savart Law

Wire Resistance

Formula: R = ρ·l / A

Finds resistance of a wire from length, area, and resistivity.

ρ (Ω·m):l (m):
A (m²):R (Ω):

Q Factor

Formula: Q = f0/Δf    or    Q = XL/R at f0

Calculates quality factor of a resonant circuit.

f0 (Hz): Δf (Hz):
R (Ω): L (µH):
Q:

Reactance

Formula: XC = 1/(2πfC),   XL = 2πfL

Computes capacitive and inductive reactance at frequency (Xc, Xl).

f (Hz): C (µF):
L (µH): XC (Ω):
XL (Ω):

Inverting Op-Amp Amplifier

Input Resistor
Rin:
Feedback Resistor
Rf:
Input Voltage
V
Vout: —   |   Gain: —
- + Blue = Input • Yellow = Output Model assumes infinite gain, no saturation.
Vout vs Vin
Ideal Op-Amp Model:
Gain = - Rf / Rin
Vout = Gain ⋅ Vin
Note: Real op-amps have bandwidth limits, offsets, and saturation; this shows ideal linear inversion.

Zener Diode Shunt Regulator

Zener Voltage
Vz:
Series Resistor
Rs:
Load
Rl:
Input Voltage
V
Vout: —   |   Iz: —   |   il: —   |   PRs: —   |   Pz: —
Blue = Input • Yellow = Output • Bar shows regulation (Vout/Vz) Adjust Vin to see regulation; Model assumes sharp breakdown at Vz.
Vout vs Vin
Ideal Zener Model:
If Vin ≤ Vz or (Vin > Vz and (Vin - Vz)/Rs < Vz/Rl): Vout = Vin ⋅ Rl / (Rs + Rl)
Else: Vout = Vz, Iz = (Vin - Vz)/Rs - Vz/Rl ≥ 0
Note: Real Zeners have knee and dynamic resistance; this shows ideal shunt regulation.

LED Matrix Font / Pattern Generator (Reversible)

Matrix:
Binary (rows)
Hex (C array)

RC Filter 1st–4th Order, Butterworth

Mode
Order
Selected: 2-order
Resistors & Capacitors (per section)
R:
C:
Frequency Test
Hz
fc (per section): —   |   |H(f)|: —   |   Phase: —
Blue = Input • Yellow = Output • Bar shows |H(f)| Drag the slider to vary applied frequency
|H(f)| (dB) Phase (°)
Formulas (ideal Butterworth Nth-order):
Cutoff per section: fc = 1 / (2πRC)
Low-pass: |H| = 1 / √(1 + (f/fc)2N), φ = −N·atan(f/fc)
High-pass: |H| = (f/fc)N / √(1 + (f/fc)2N), φ = N·(atan(f/fc) − 90°)

Note: Actual equal-section passive cascades may differ, this just illustrates the sharper knee when using an increasing filter order.

Rectangular ↔ Polar (Complex Numbers)

Quick Overview

Convert a complex number between rectangular form a + jb and polar form r ∠ θ. Type values in either panel and results update automatically.

  • Rect → Polar: r = √(a²+b²), θ = atan2(b,a)
  • Polar → Rect: a = r·cos(θ), b = r·sin(θ)
  • Angle can be shown in degrees or radians. Use DPs for rounding.
Rectangular (a + jb)
a (Real):
b (Imag):
Polar (r ∠ θ)
r (Magnitude):
θ (Angle):
Angle units:
Outputs
Rect:
—
Polar:
—
DPs:
     Auto-updating
Notes: θ uses atan2(b,a), so it is correct for all quadrants. Magnitude uses √(a²+b²).

RC Filter 1st Order

Mode
Resistor & Capacitor
R:
C:
Frequency Response
Hz
fc: — | |H(f)|: — | Phase: —
Blue = Input • Yellow = Output (bar shows amplitude) Drag the slider to vary applied frequency
|H(f)| (dB) Phase (°)
Formulas used:
fc = 1 / (2πRC)
|H(f)| = 1 / √(1 + (f/fc)²)
φ(f) = −tan⁻¹(f/fc)
At f = fc, |H| = −3 dB and φ = −45°.

Resistor Colour Code to Value

Band count
Result
Pick digits and multiplier.
Significant digits
Multiplier / Tolerance / Tempco

PPM/DegC

Formula: ΔV = Vnom × (PPM × ΔT) / 10⁶

Calculate the change in value of any nominal value (voltage etc) for every degC change.
Note: % = ppm / 10000
Nominal Value:
PPM:
Tested range degC:
Result: Variation per degC:
Result: Variation across tested temp range:

Voltage Regulator Capacitor Designer/Helper

Topology:
Vin / Vout: V  /  V
Iload (A):
Switching fsw / L: /
Allowed ΔVout (Vpp):
ESR estimate (Ω): per capacitor
Cap type & derating:  Effective factor: (e.g. 0.5–0.7 MLCC at bias)
E-series & units:
Ratings (min): Vrating headroom:  Max parts in parallel to try:
# Role N × Cap (nom) Ceff total ESR total Est. ripple / note
Fill the inputs and click Calculate…
Instructions & field help
  • Topology – Choose LDO for linear regulators (no inductor), or Buck/Boost for switchers.
  • Vin / Vout – Input/output voltages in volts (V).
  • Iload – Maximum DC load current in amps (A).
  • Switching fsw / L – Converter switching frequency (Hz) and inductor value (H). Used to estimate inductor ripple current.
  • Allowed ΔVout – Peak-to-peak ripple or droop you can tolerate at Vout (Vpp). If unsure, 1–2% of Vout is a common starting point.
  • ESR estimate (Ω) – ESR of a single chosen capacitor at the relevant frequency. Parallel parts reduce ESR: ESRtotal ≈ ESReach/N.
  • Cap type & derating – Picks technology and the effective factor applied to nominal capacitance:
    • MLCC: capacitance falls with DC bias & temp; use 0.5–0.7 as a realistic effective factor at working voltage.
    • Electrolytic: value is close to nominal; use 0.8–1.0. Check ripple current rating.
    • Tantalum: use 0.8–1.0; ensure surge/derating per datasheet.
  • E-series & units – Rounds suggestions to E6/E12/E24 preferred values in the unit you like (nF/µF/mF).
  • Voltage rating headroom – Minimum ratio of part rating to the highest DC across it. Example 1.25× on a 12 V rail ⇒ ≥ 15 V rated parts.
  • Max parts – Upper bound on how many caps in parallel to consider.
What the results mean
  • N × Cap (nom) – Number of parallel parts and their nominal value (before derating).
  • Ceff total – Effective capacitance available after derating and paralleling:
    Ceff,total = N × Cnom × effective_factor.
  • ESR total – Parallel ESR estimate:
    ESRtotal ≈ ESReach / N.
  • Est. ripple / note – First-order ripple (or hold-up) estimate and any rating reminders.
How ripple is estimated
Switching (Buck/Boost) – Output ripple is the sum of a capacitive term and an ESR term:
• Inductor ripple current, rough:
Buck: ΔIL ≈ (Vin − Vout) · D / (L · fsw)
Boost: ΔIL ≈ Vin · D / (L · fsw), where D = 1 − Vin/Vout
• Ripple from capacitance: ΔVC ≈ ΔIL / (8 · C · fsw)
• Ripple from ESR: ΔVESR ≈ ΔIL · ESRtotal
• The tool sizes Cout so ΔVESR + ΔVC ≤ ΔVout, allowed.
Choosing Cin vs Cout
  • Cout – Controls output ripple and load-step droop. Favor low ESR near the regulator. MLCCs excel for high-frequency ripple; add an electrolytic for bulk if needed.
  • Cin – Decouples the switch/input pin. For bucks, input RMS current can be significant (~worst near D≈0.5). Place low-ESR MLCC(s) close to the switch, and ensure the voltage rating headroom.
Practical tips
  • Bias derating (MLCC): 10–22 µF parts can lose 30–60% at working voltage; the effective factor accounts for this.
  • ESR vs stability: Many LDOs require a minimum ESR; some switching controllers specify Cout ESR ranges—always check the datasheet.
  • Ripple current rating: For electrolytics/tantalum, ensure the capacitor’s ripple current rating exceeds the expected ripple current.
  • Thermal & layout: Keep high-di/dt loops tight. Put Cin right at the switch pins; pour ground and use short, wide traces.
  • Validation: Measure with a short ground spring on the scope probe to avoid ground-lead artifacts.

These are first-order estimates. Final values must satisfy your regulator’s datasheet (minimum Cout, ESR windows, stability, and ratings).

Non-Inverting Op-Amp Amplifier

Ground Resistor
Rin:
Feedback Resistor
Rf:
Input Voltage
V
Vout: —   |   Gain: —
- + Blue = Input • Yellow = Output Model assumes infinite gain, no saturation.
Vout vs Vin
Ideal Op-Amp Model:
Gain = 1 + Rf / Rin
Vout = Gain ⋅ Vin
Note: Real op-amps have bandwidth limits, offsets, and saturation; this shows ideal linear amplification.

PPM

Formula: PPM = (ΔV / Vnom) × 10⁶

Calculate the voltage deviation/ppm based on the given inputs.
Note: 1 ppm = 0.0001%
Nominal Voltage (V):
PPM:
Voltage Deviation (V):
Voltage Deviation (µV):
Voltage Deviation (nV):

Temperature Coefficient of Resistance (TCR)

Formula: RT = R0[1 + α(T − T0)]

Finds resistance change with temperature.

R0 (Ω):α (1/°C):
T (°C):T0 (°C):
RT (Ω):

Op-Amp Gain (inverting)

Formula: Av = –Rf / Rin

Calculates the gain of an inverting amplifier.

Rf Ohm:
Rin Ohm:
Gain:

Op-Amp Gain (non-inverting)

Formula: Av = 1 + (Rf / Rin)

Calculates the gain of a non-inverting amplifier.

Rf Ohm:
R3 Ohm:
Gain:

Time / Hz

Formula: f = 1 / T    and    T = 1 / f

Converts between frequency and period.

Convert Time & Frequency.
Freq Hz:
Period mS:
Period mS:
Freq Hz:

Impedance of R, L, C at frequency f (series)

Formula: Z = √[ R² + (ωL – 1/ωC)² ]

Phase: θ = tan⁻¹((ωL – 1/ωC) / R)

Calculates total impedance of series R, L, C.

Series impedance at frequency f
R (Ω):f (Hz):
L (H):C (F):
XL (Ω):XC (Ω):
|Z| (Ω):∠ (deg):

Energy in a Capacitor

Formula: E = ½·C·V²

Calculates stored energy from C and V.

C (µF): V (V):
E (J):

Energy in an Inductor

Formula: E = ½·L·I²

Calculates stored energy from L and I.

L (µH): I (A):
E (J):

SNR (in dB)

Formula: SNRdB = 20·log₁₀(Vs/Vn)

Converts voltage ratio into SNR dB.

Vs (V):Vn (V):
SNR (dB):

LC Resonant Frequency

Formula: f₀ = 1 / (2π√(LC))

Finds the resonant frequency of an LC circuit.

LC resonant frequency (f = 1 / (2π√(LC)))
L (H):
C (F):
f (Hz):

RC Filter 1st Order

Formula: fc = 1 / (2πRC)

Enter any two fields (R in Ω, C in uF, F in Hz), then click Solve.
R (Ω):
C (uF):
F (Hz):

Power Supply Ripple (with DC voltage)

Formulae: Vr(pp) ≈ I / (fripple · C),   fripple = fline (half-wave) or 2·fline (full-wave)

Enter load current (or VDC + R), line frequency, capacitance (µF), and rectifier type. Optionally enter VDC to see ripple % and estimated Vmin/Vmax.

VDC (V): I (A):
R (Ω): fline (Hz):
C (µF): Rectifier:
fripple (Hz): Vr(pp) (V):
Ripple (% of VDC): Vmin / Vmax (V): /

Rectifier Capacitor Ripple

Formula: Vripple ≈ I / (f·C)

Estimates ripple voltage from load and capacitance.

I (A): f (Hz):
C (µF): Vripple (V):

Wavelength ↔ Frequency ↔ Signal Speed

Formula: λ = v/f    f = v/λ    v = fλ

Relates signal speed, wavelength, and frequency.

Wavelength / Frequency / Velocity (enter any two)
f (Hz):
λ (m):
v (m/s):

Quarter-Wave Resonator

Formula: l = v / (4·f)

Calculates resonant length of a λ/4 resonator.

v (m/s):f (Hz):
l (m):

Transmission Line Impedance

Formula: Z0 = √(L/C)   (L, C per unit length)

Finds characteristic impedance from L and C.

L (H/m):C (F/m):
Z0 (Ω):

Skin Depth

Formula: δ = √(2ρ / (ωμ)), with μ = μ₀μr

Computes AC current penetration depth in conductors.

ρ (Ω·m):f (Hz):
μr:δ (m):

Current Density

Formula: J = I / A

Calculates current per unit area.

I (A): A (m²):
J (A/m²):

Reactance

Quick Overview

Reactance is the AC “resistance” of reactive parts: Capacitive XC = 1/(2πfC) (decreases with f)   |   Inductive XL = 2πfL (increases with f). Enter frequency plus C and/or L; if both are given, series resonance f₀ is shown.

  • Units supported: Hz/kHz/MHz, pF…F, µH…H. Scientific notation like 2.2e-6 works.
  • Outputs shown in Ω/kΩ/MΩ. Plot is log–log across ±2 decades around the entered frequency.
Frequency (f): Capacitance (C):
Inductance (L): DPs & Units:
XC: XL:
Solve to draw X(f)

dBm ↔ mW / W conversions

Formula: P(dBm) = 10·log₁₀(PmW / 1mW)

Formula: P(mW) = 10^(P(dBm)/10)

Formula: P(W) = P(mW) / 1000

Converts between dBm, milliwatts, and watts.

dBm ↔ mW / W
dBm:
mW:
W:

Battery Life Estimator

Formula: t = (Capacity / Load) × (Efficiency / 100)

Estimates operating time from capacity and load.

Battery life estimate
Capacity (mAh):Load (mA):
Efficiency (%):Hours:
Days:

Power Dissipation

Formula: P = VI    or    P = I²R    or    P = V²/R

Computes electrical power from V, I, or R.

Power (enter any two: V, I, R)
V (V):I (A):
R (Ω):P (W):

dB Conversions (power & voltage ratios)

Formula: dB (power) = 10·log₁₀(P₂/P₁)

Formula: dB (voltage) = 20·log₁₀(V₂/V₁)

Converts power/voltage ratios to decibels.

dB conversions (power & voltage ratios)
Power ratio (P2/P1):dB (power):
Voltage ratio (V2/V1):dB (voltage):

Duty Cycle ↔ On/Off Time

Formula: D = (ton/T) × 100%

Formula: ton = D·T,    toff = T – ton

Converts between duty %, on-time, and off-time. Enter f or T plus duty.

Duty cycle calculator (enter f or T, plus duty %)
f (Hz):T (s):
Duty (%):
Ton (s):Toff (s):

mm to mils

Formula: mils = mm / 0.0254    or    mm = mils × 0.0254

Converts metric to imperial PCB dimensions.

mils to mm / mm to mils.
mm
mils

Digital Multimeter — Uncertainty Specifications

Quick Overview

This tool estimates the measurement uncertainty of a DMM for a given range and reading, using datasheet-style specifications of the form ±(ppm of Reading + ppm of Full-scale), plus optional calibration and temperature terms. It works for voltage, current and resistance ranges, and supports a 3458A-style temperature coefficient of (ppm of reading + ppm of range) per °C.

  • Range full-scale (FS): Enter the range value (e.g. 10) and choose the unit (V, mA, kΩ, etc.).
  • Reading (R): Enter the reading in the same unit as FS (the unit label updates automatically).
  • Applied / Ambient Temp: The temperature at which the measurement is made.
  • Reference Temp (Tref): The reference temperature of the spec (usually 23 °C or 25 °C).
  • Spec set: Which datasheet column you are using: 24 Hour, 1 Year, or Custom.
  • 24h / 1y / Custom ppmR & ppmFS: Copy the accuracy line from the datasheet, interpreted as ±(ppmR·R + ppmFS·FS).
  • Calibration uncertainty: Extra ppm of reading from the Cal. lab (often the “Typical Calibration Uncertainty” column).
  • Temp coefficient (per °C): Enter ppm of reading and ppm of range per °C (e.g. 3458A style: “(ppm of reading + ppm of range)/°C”).

Error model & results

  • |ΔT|: |Ambient − Tref| (shown in °C).
  • ER (reading term): ppmR · R / 10⁶.
  • EFS (full-scale term): ppmFS · FS / 10⁶.
  • Ecal (calibration): ppmCal · R / 10⁶.
  • ET (temperature): (ppmTC_R·R + ppmTC_FS·FS) · |ΔT| / 10⁶.
  • Worst-case |E|: |ER| + |EFS| + |Ecal| + |ET| (same units as FS / R).
  • RSS “typical” (root-sum-square) |E|: √(ER² + EFS² + Ecal² + ET²).
  • Displayed (WC): R ± |E|, i.e. the reading range that covers the worst-case error.
  • Total spec (ppm): The total worst-case error expressed in ppm of the reading: |E| / R × 10⁶. This normalizes the uncertainty so different readings, ranges, and functions can be compared directly.

Note: Leave unused entries blank or set to zero.
Inputs
Range full-scale (FS):
Reading (R):
V
Applied / Ambient Temp:
°C
Reference Temp (Tref):
°C
Spec set:
24h: ±(ppmR + ppmFS)
ppmR ppmFS
1y: ±(ppmR + ppmFS)
ppmR ppmFS
Custom:
ppmR ppmFS
Calibration uncertainty:
ppm of reading
Temp coefficient (per °C):
ppmR/°C ppmFS/°C
Results
|ΔT| = |Ambient − Tref|:
-
ER (reading term):
-
EFS (full-scale):
-
Ecal:
-
ET (temp):
-
Worst-case |E|:
-
RSS “typical” |E|:
-
Displayed (WC):
-
Total spec (ppm):
-
Error term formulas:
• ER = (ppmR × R) / 10⁶ Reading-dependent uncertainty
• EFS = (ppmFS × FS) / 10⁶ Full-scale (range) uncertainty
• Ecal = (ppmCal × R) / 10⁶ Calibration reference contribution
• ET = [(ppmTCR × R) + (ppmTCFS × FS)] × |ΔT| / 10⁶ Temperature coefficient applied to the reading and the range

Combination rules:
• Worst-case: |ER| + |EFS| + |Ecal| + |ET| All error sources assumed to add in the same direction
• RSS (typical): √(ER² + EFS² + Ecal² + ET²) Statistical combination; typical real-world performance

SMPS — Duty, Inductor Ripple & Output Ripple

Quick Overview

A buck SMPS reduces a higher input voltage Vin to a lower Vout using a switch, diode/MOSFET, inductor, and output capacitor. This tool assumes ideal parts and CCM (the inductor current never reaches zero). Results update automatically as you type.

  • fs: Switching frequency.
  • Duty D: On-time fraction (ideal buck: D ≈ Vout/Vin).
  • ΔIL (pp): Inductor current ripple, peak-to-peak.
  • Ipk / Ivalley: Max/min inductor current each cycle (average equals load current).
  • L (~30% ripple): Inductance that gives ~30% ripple at the entered load and fs.
  • ΔVESR: Ripple from the capacitor ESR (ΔV = ΔIL · ESR).
  • ΔVC: Capacitive ripple from charge/discharge (ΔV = ΔIL / (8 · fs · C)).
  • ΔVtotal (pp): Simulated time-domain ripple (ESR + capacitive).
  • CCM check: CCM holds if Iout > ΔIL/2.
Inputs
VIN:
V
VOUT:
V
IOUT:
A
fs:
L:
C (output):
ESR (cap):
Vripple target:
mVpp
Results (ideal)
fs:
-
Duty D:
-
ΔIL (pp):
-
Ipk:
-
Ivalley:
-
L (~30% ripple):
-
ΔVESR:
-
ΔVC:
-
ΔVtotal (pp):
-
C needed @ target:
-
Inductor Current (IL) Scale: pp: -
Output Voltage Ripple Scale: pp: -
SW Node Voltage (Vsw)

555 Timer (Astable) - Mark/Space & Duty

Timing Components
RA:
RB:
C:
Results
f:
—
Duty:
—
Mark:Space:
—
tH:
—
tL:
—
T:
—
f = 1.44 / ((RA + 2RB)·C), tH = 0.693(RA + RB)·C, tL = 0.693 RB·C, D = (RA + RB)/(RA + 2RB)
Schematic — 555 Astable
1 2 3 4 GND RESET OUT TRIG CTRL V CC DIS THR 8 6 7 5 V CC GND RA C RB 10nF Out

555 Timer (Astable) Frequency & Duty

Formula: f = 1.44 / ((RA + 2RB)C)

Duty: D = (RA + RB) / (RA + 2RB) × 100%

tH: 0.693(RA + RB)C,    tL: 0.693RBC

Calculates timing values for a 555 astable.

555 Timer (astable) — RA, RB (Ω), C (uF)
RA (Ω):RB (Ω):
C (uF):
f (Hz):Duty (%):
tH (s):tL (s):
T (s):

Joule ↔ Watt-hour

Formula: 1 Wh = 3600 J

Converts between Joules and Watt-hours.

Joule ↔ Watt-hour
Energy (J):
Energy (Wh):

Voltage Divider

Formula: Vout = Vin × (R₂ / (R₁ + R₂))

Enter any three fields and leave one blank; click Solve to calculate the missing one.
If all four are filled, Solve re-calculates the last-solved field (or Vout by default).
Both positive and negative Input.V values are accepted.

Input.V:
R1:
R2:
Output.V:
DPs:   

Joule’s Law — P = I²R

Quick Overview

Joule’s Law defines the electrical power dissipated as heat in a conductor when current flows through it. The law states that the power (P) developed in a resistor is proportional to the square of the current (I) and the resistance (R): P = I²R. This principle forms the basis for calculating energy losses in resistors, heating elements, and conductors.

  • Formula: P = I² × R
  • P = Power (Watts)
  • I = Current (Amperes)
  • R = Resistance (Ohms)
Power (P): W
Current (I): A
Resistance (R): Ω
Example: If a current of 2.5 A flows through a 4 Ω resistor, then P = (2.5)² × 4 = 25.0 W.

Lenz’s Law

Quick Overview

Lenz’s Law describes the direction of an induced electromotive force (EMF) caused by a changing magnetic field. It states that the induced EMF will always act to oppose the change in magnetic flux that produced it. The negative sign in the equation reflects this opposition — ensuring energy conservation and preventing self-reinforcement of the magnetic field.

  • Formula: E = −N × (dΦ/dt)
  • E = Induced EMF (Volts)
  • N = Number of turns in the coil
  • dΦ/dt = Rate of change of magnetic flux (Webers per second)
Induced EMF (E): V
Coil Turns (N):
Rate of Flux Change (dΦ/dt): Wb/s
Example: If a 200-turn coil experiences a flux change rate of 0.015 Wb/s, then E = −200 × 0.015 = −3.0 V (the negative sign shows the opposing direction).

Kirchhoff’s Laws

KCL: ΣIin − ΣIout = 0   |   KVL: ΣV(loop) = 0

Quick Overview

Kirchhoff’s Laws are two fundamental principles of electrical circuit analysis. They describe how current and voltage distribute within any network. Kirchhoff’s Current Law (KCL) states that the total current entering a junction equals the total current leaving it, ensuring charge conservation. Kirchhoff’s Voltage Law (KVL) states that the sum of all voltage rises and drops around a closed loop is zero, conserving energy. Together, these laws provide the foundation for solving even the most complex DC and AC circuits.

  • Kirchhoff’s Current Law (KCL): At any node, total current entering = total current leaving.
  • Kirchhoff’s Voltage Law (KVL): Around any closed loop, total voltage drops = total rises.

KCL — Node Current Balance

Use sign convention: + = current into node, − = out of node. Leave one field blank to solve the unknown, or fill all to check ΣI = 0.

DPs: Units:
Example: +2.5 A, −1.2 A, ? → Unknown = −(2.5 − 1.2) = −1.3 A (i.e. 1.3 A out).

KVL — Loop Voltage Sum

Use sign convention: + = drop, − = source/rise. Leave one field blank to solve the missing voltage or fill all to verify ΣV = 0.

DPs: Units:
Example: −12 V (source), +7.2 V (drop), ? → Unknown = −(−12 + 7.2) = +4.8 V (drop).

Tips & FAQ

  • Use scientific notation (e.g. 2.5e-3 for 2.5 mA).
  • KCL satisfied → currents balance to 0 A.
  • KVL satisfied → voltage drops and rises sum to 0 V.
  • Check units: mA vs A, mV vs V, etc.

Parallel Resistors

Formula: 1/Req = 1/R₁ + 1/R₂ + … + 1/Rn

R1: R2:
R3: R4:
R5: R6:
R7: R8:
Total Resistance:
DPs:   Output units:   
Reverse (desired total): E-series: Maximum no. resistors to combine:

LM317

Formula (LM317): Vout = Vref(1 + R₂/R₁) + Iadj·R₂

Calculates output voltage of LM317 regulator.

Vref (V): Iadj (A):
R1 (Ω): R2 (Ω):
Vout (V):

LM337

Formula (LM337): Vout = Vref(1 + R₂/R₁) + Iadj·R₂   (typ. Vref ≈ –1.25 V)

Calculates output voltage of LM337 regulator.

Vref (V): Iadj (A):
R1 (Ω): R2 (Ω):
Vout (V):

RC Charge/Discharge

Quick Overview

In a simple RC circuit, the capacitor voltage follows an exponential curve with time constant τ = R × C. A general form that covers both charging and discharging is: VC(t) = Vf + (V0 − Vf) · e−t/(RC), where V0 is the initial capacitor voltage at t=0, and Vf is the final voltage the capacitor is heading toward (for charging, Vf=VS; for discharging to ground, Vf=0).

  • Charging: VC(t) = VS − (VS − V0) e−t/RC
  • Discharging: VC(t) = V0 e−t/RC (toward 0 V)
  • At t = τ, charging reaches ≈63.2% of the final step; discharging falls to ≈36.8% of the initial value.
  • Enter values using handy units (kΩ, µF, ms, etc.). Use scientific notation like 2.2e-6 if you prefer.
Mode:
Supply (VS): (ignored in Discharge) Initial (V0):
Resistance (R): Capacitance (C):
Time (t): Target VC (optional):
DPs:   
Solve to draw V(t)

Faraday’s Law of Electromagnetic Induction

Quick Overview

Faraday’s Law describes how a changing magnetic field induces an electromotive force (EMF) in a coil or conductor. The magnitude of the induced EMF is proportional to the rate of change of magnetic flux and the number of turns in the coil: E = −N × (ΔΦ / Δt). The negative sign represents Lenz’s Law — the induced EMF opposes the change that produced it.

  • E = Induced EMF (Volts)
  • N = Number of turns in the coil
  • ΔΦ = Change in magnetic flux (Webers)
  • Δt = Time interval (seconds)
  • Enter any three values to solve for the fourth.
EMF (E): V Turns (N):
Flux Change (ΔΦ): Wb Time Interval (Δt): s
DPs:   
Example: N = 200 turns, ΔΦ = 0.015 Wb, Δt = 0.05 s → E = N × (ΔΦ / Δt) = 200 × (0.015 / 0.05) = 60 V.

Ohm’s Law

Quick Overview

Ohm’s Law relates voltage (V), current (I), and resistance (R) in any electrical circuit: V = I × R, I = V / R, R = V / I. Power ties in via P = V × I = I²R = V²/R. Enter any two values to compute the other two.

  • Use scientific notation (e.g. 2.5e-3 for 2.5 mA).
  • Pick convenient units from the dropdowns; results are written using the selected units.
  • If you provide more than two inputs, the first valid pair in priority (V&I → V&R → I&R → P&V → P&I → P&R) is used.
Voltage (V): Current (I):
Resistance (R): Power (P):
DPs:   
Example: V = 12 V, R = 4.7 kΩ → I = 12 / 4700 = 2.553 mA, P = 12 × 2.553 mA ≈ 30.6 mW.

Biot–Savart Law

Quick Overview

The Biot–Savart Law gives the magnetic field contribution from current elements: dB = (μ₀ μr / 4π) · (I dℓ × r̂) / r².
Biot-Savart Law is one of the big four Maxwell's equations.
For common symmetric shapes this integrates to compact formulas:

  • Loop (center): B = μ₀ μr N I / (2R)
  • Loop on-axis (distance x): B = μ₀ μr N I R² / [2(R² + x²)^{3/2}]
  • Finite straight wire (length L, point at r from midpoint): B = (μ₀ μr I / 4πr) · (L / √(r² + (L/2)²))
  • Circular arc (angle φ): B = μ₀ μr N I φ / (4πR)   (φ in radians)
Constants: μ₀ = 4π×10⁻⁷ H/m. Use μr=1 for air/vacuum. Outputs show both B (tesla) and H (A/m), with B = μ·H.
Geometry:
μr (relative): (dimensionless)
Turns N: Current I:
Radius R: Field at loop center
Turns N: Current I:
Radius R: Axial x:
Current I: Length L:
Perp. distance r: (Point lies on line normal through wire midpoint)
Turns N: Current I:
Radius R: Angle φ (deg):
DPs:   
B-field: H-field:
Solve to visualize

Ampère’s Law

Quick Overview

Ampère’s Law (magnetostatics) relates the circulation of the magnetic field around a closed loop to the total current enclosed: ∮ B·dℓ = μ₀ μr Ienc.
Ampère's Law is one of the big four Maxwell's equations.
With symmetry, this gives handy field formulas:

  • Long straight wire: B = μ₀ μr I / (2π r)
  • Long solenoid (inside): B = μ₀ μr n I, where n = N/L
  • Toroid (mean radius r): B(r) = μ₀ μr N I / (2π r)
Constants: μ₀ = 4π×10⁻⁷ H/m. Use μr=1 for air/vacuum. Outputs show both B (tesla) and H (A/m), with B = μ·H.
Geometry:
μr (relative): (dimensionless, e.g. air=1, ferrite ~ 100–2000)
Current I: Radius r:
Turns N: Length L:
Current I: (Assumes long solenoid, field near center)
Turns N: Current I:
Radius r (point): (Field valid for r between inner & outer radii)
DPs:   
B-field: H-field:
Solve to visualize

Gauss’s Law

Quick Overview

Gauss’s Law relates total electric flux through a closed surface to the enclosed charge: ∮ E·dA = Qenclosed/ε₀. It’s most useful for highly symmetric fields.
Gauss's Law is one of the big four Maxwell's equations.

  • Flux–Charge: Φ = Q/ε₀,   Q = ε₀Φ
  • Symmetric fields: Sphere: E = Q/(4π ε₀ r²) · r̂   |   Line: E = λ/(2π ε₀ r) · r̂   |   Plane: E = σ/(2ε₀) n̂
  • ε₀ = 8.854 187 812 8 × 10⁻¹² F·m⁻¹
Mode:
Geometry:
Charge Q: Flux Φ: (N·m²/C)
Charge Q (sphere): Radius r (sphere):
Line charge λ: Radius r (line):
Cylinder length L: (Affects flux via Qenc=λ·L; E depends only on r)
Surface charge σ: Area A (optional):
DPs:   
Electric field E: Flux Φ:
Solve to visualize

Coulomb’s Law

Quick Overview

Coulomb’s Law describes the electric force between two point charges. The magnitude of the electrostatic force is proportional to the product of the charges and inversely proportional to the square of their separation distance.
Coulomb's Law is one of the big four Maxwell's equations.

Formula: F = k · |q₁ · q₂| / r²
where k = 8.9875×10⁹ N·m²/C², q₁ and q₂ are charges in coulombs, and r is distance in meters.

  • Positive force ⇒ repulsion (like charges)
  • Negative force ⇒ attraction (opposite charges)
Charge q₁ (C):
Charge q₂ (C):
Distance r (m):
Force (N):
Solve to visualize

Zener Diode

Formula: Vout ≈ VZ,    Rs = (Vin – VZ) / (IZ + IL)

Calculates series resistor and power dissipation.

Max Input: Volts
Min Input: Volts
Output: Volts
Load: mA
Results:
Resistor - Ohms
Resistor - Watts
Zener - Volts
Zener - Watts

Decimal ↔ Scientific converter

Converter: Decimal ↔ Scientific (a × 10b)

Converts between decimal and scientific notation.

Decimal:
Mantissa (a):
Exponent (b):
Sig. digits:

DC Power Supply Efficiency

Formula: η (%) = 100 · (VoutIout) / (VinIin)

Vin (V): Iin (A):
Vout (V): Iout (A):
Pin (W): Pout (W):
η (%) : Loss (W):

Voltage Drop (wire/cable), % drop & loss

Formula: R = ρ·L/A,   Vdrop = I·R,   Ploss = I²R

Current (A): Length one-way (m):
Area (mm²): Material:  
System V (optional):
Resistance (Ω): Vdrop (V):
Ploss (W): % of System V:

Decimal ↔ mA, µA/uA, nA, pA and mV, µV/uV, nV, pV ↔ Scientific

Converter: mA / µA / nA / pA and mV / µV / nV / pV ↔ Scientific (a×10b)

Converts SI-prefixed values to/from scientific notation.

Value with unit:
Scientific (a × 10^b): × 10^  Unit:
SI (base):
Best prefix:

RLC Impedance (series/parallel) → |Z| and phase

Mode: f (Hz):
R (Ω): L (H):
C (F): |Z| (Ω):
Phase (°):

RC Charging/Discharging (time ↔ % of Vin)

R (Ω): C (F):
Target % of Vin: Time t (s):

LED Series Resistor

Vs (V): Vf (V):
If (mA): LEDs in series (N):
Resistor R (Ω): Resistor power (W):

Capacitor Code ↔ Value

Formula: 3-digit EIA capacitor code → pF / µF, and reverse. Example 104 = 100,000 pF = 0.1 µF

Code (3-digit): or Value (µF):
Result:

Resistor Colour Code ↔ Value

Formula: Resistor colour code (4 / 5 / 6-band). Works in both directions — enter resistance or colour bands.

Resistance (Ω): Bands:
Tolerance (%): Temp Coeff (ppm/°C):
Colours:

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Copyright © Ian Johnston - Do not copy or reproduce.

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