Electrical calculators. 94 tools for everyday electrical maths.

Foundations

I = \frac{Q}{t}

FoundationsCharge transferred

Q = I t

FoundationsOhm’s law: current

I = \frac{V}{R}

FoundationsOhm’s law: voltage

V = I R

FoundationsOhm’s law: resistance

R = \frac{V}{I}

FoundationsCable area: mm² to m²

A_{m²} = A_{mm²} \times 10^{- 6}

FoundationsCircular conductor area

A = \frac{π d^{2}}{4}

Power and energy

Power and energyElectrical power: VI

P = V I

Power and energyResistive heating: I²R

P = I^{2} R

Power and energyResistive power: V²/R

P = \frac{V^{2}}{R}

Power and energyEnergy in joules

E = P t

Power and energyEnergy from voltage and current

E = V I t

Power and energyEnergy in kilowatt-hours

E = \frac{P \times t_{h}}{1000}

Power and energyKilowatt-hours from V and I

E_{kWh} = \frac{V I t_{h}}{1000}

Power and energyEnergy cost

cost = \frac{P \times t_{h} \times c}{1000}

Circuits and conductors

Circuits and conductorsResistance and resistivity

R = \frac{ρ l}{A}

Circuits and conductorsSeries resistance

R_{t} = R_{1} + R_{2} + R_{3}

Circuits and conductorsParallel resistance

\frac{1}{R_{t}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}}

Circuits and conductorsTwo parallel resistors

R_{t} = \frac{R_{1} R_{2}}{R_{1} + R_{2}}

Circuits and conductorsSeries–parallel resistance

R_{t} = R_{1} + \frac{R_{2} R_{3}}{R_{2} + R_{3}}

Circuits and conductorsVoltage divider

V_{2} = V_{s} \times \frac{R_{2}}{R_{1} + R_{2}}

Circuits and conductorsCurrent divider

I_{1} = I_{t} \times \frac{R_{2}}{R_{1} + R_{2}}

Circuits and conductorsKirchhoff: current balance

\sum I_{in} = \sum I_{out}

Circuits and conductorsKirchhoff: voltage balance

\sum_{loop} V = 0

Circuits and conductorsResistance and temperature

R_{2} = R_{1} [1 + α (T_{2} - T_{1})]

Circuits and conductorsCurrent density

J = \frac{I}{A}

Capacitance and inductance

Capacitance and inductanceCapacitance and charge

Q = C V

Capacitance and inductanceCapacitor energy

E = \frac{1}{2} C V^{2}

Capacitance and inductanceCapacitors in parallel

C_{t} = C_{1} + C_{2} + C_{3}

Capacitance and inductanceTwo capacitors in series

C_{t} = \frac{C_{1} C_{2}}{C_{1} + C_{2}}

Capacitance and inductanceRC time constant

τ = R C

Capacitance and inductanceCapacitor discharge voltage

V (t) = V_{0} e^{- t / (R C)}

Capacitance and inductanceInductor energy

E = \frac{1}{2} L I^{2}

Capacitance and inductanceRL time constant

τ = \frac{L}{R}

AC foundations

AC foundationsFrequency from period

f = \frac{1}{T}

AC foundationsPeriod from frequency

T = \frac{1}{f}

AC foundationsWave speed

v = f λ

AC foundationsWavelength

λ = \frac{v}{f}

AC foundationsPeak voltage

V_{p} = \sqrt{2} \times V_{rms}

AC foundationsRMS voltage

V_{rms} = \frac{V_{p}}{\sqrt{2}}

AC foundationsPeak-to-peak voltage

V_{pp} = 2 V_{p}

AC foundationsRMS current

I_{rms} = \frac{I_{p}}{\sqrt{2}}

AC foundationsInductive reactance

X_{L} = 2 π f L

AC foundationsCapacitive reactance

X_{C} = \frac{1}{2 π f C}

AC foundationsSeries RLC impedance

| Z | = \sqrt{R^{2} + {(X_{L} - X_{C})}^{2}}

AC foundationsAC current from impedance

I = \frac{V}{| Z |}

AC foundationsSeries impedance phase angle

φ = \arctan [\frac{X_{L} - X_{C}}{R}]

AC foundationsLC resonant frequency

f_{0} = \frac{1}{2 π \sqrt{L C}}

AC foundationsWave speed in a medium

v = \frac{299792458}{\sqrt{ε_{r} \times μ_{r}}}

AC foundationsInstantaneous sine-wave voltage

v = V_{p} \times \sin θ

AC foundationsMean of a rectified sine wave

V_{mean} = \frac{2 V_{p}}{π}

Magnetism

MagnetismMagnetic flux

Φ = B \times A \times \cos θ

MagnetismInduced voltage: changing flux

| e | = N \times \frac{| Δ Φ |}{Δ t}

MagnetismVoltage from conductor motion

e = B \times l \times v

MagnetismForce on a conductor

F = B \times I \times l \times \sin θ

AC power

AC powerSingle-phase active power

P = V \times I \times PF

AC powerSingle-phase apparent power

S = V \times I

AC powerPower factor from measured power

PF = \frac{P}{S}

AC powerReactive power and the power triangle

Q = \sqrt{S^{2} - P^{2}}

AC powerBalanced three-phase active power

P = \sqrt{3} \times V_{L} \times I_{L} \times PF

AC powerBalanced three-phase apparent power

S = \sqrt{3} \times V_{L} \times I_{L}

AC powerStar connection: line and winding voltage

V_{L} = \sqrt{3} \times V_{ph}

AC powerDelta connection: line and winding current

I_{L} = \sqrt{3} \times I_{ph}

AC powerPower factor correction: required kvar (P in kW)

Q_{c} = P \times (\tan φ_{1} - \tan φ_{2})

Motors and transformers

Motors and transformersSynchronous speed

n_{s} = \frac{120 \times f}{p}

Motors and transformersInduction-motor slip

s % = \frac{n_{s} - n_{r}}{n_{s}} \times 100

Motors and transformersShaft torque from power and speed

T \approx \frac{9550 \times P_{out}}{1000 \times n}

Motors and transformersMotor efficiency and losses

η = \frac{P_{out}}{P_{in}}

Motors and transformersThree-phase motor current from output power

I_{L} = \frac{P_{out}}{\sqrt{3} \times V_{L} \times PF \times η}

Motors and transformersTransformer voltage and turns ratio

\frac{V_{s}}{V_{p}} = \frac{N_{s}}{N_{p}}

Motors and transformersIdeal transformer current ratio

\frac{I_{p}}{I_{s}} = \frac{V_{s}}{V_{p}} = \frac{N_{s}}{N_{p}}

Lighting

LightingIlluminance from light reaching a surface

E_{avg} = \frac{Φ_{received}}{A}

LightingPoint-source illuminance and distance

E = \frac{I_{v}}{d^{2}}

LightingLumen method: estimating luminaire numbers

N = \frac{E_{m} \times A}{Φ \times UF \times MF}

LightingLighting maintenance factor

E_{m} = E_{initial} \times MF

LightingLuminaire luminous efficacy

K = \frac{Φ}{P}

LightingRoom index for utilisation data

K_{r} = \frac{L \times W}{H_{m} \times (L + W)}

Installation design

Installation designDesign current from electrical input power (single-phase)

I_{b} = \frac{P}{U \times \cos φ}

Installation designCable rating correction factors

I_{t} \geq \frac{I_{n}}{C_{a} \times C_{g}}

Installation designVoltage drop using mV/A/m

Δ U = \frac{m \times I_{b} \times L}{1000}

Installation designVoltage drop as a percentage

Δ U % = \frac{100 \times Δ U}{U_{n}}

Installation designVoltage drop with resistance and reactance (single-phase)

Δ U = \frac{2 I L (r \cos φ + x \sin φ)}{1000}

Installation designLoop impedance and operating current

Z_{s,max} = \frac{U_{0} \times C_{min}}{I_{a}}

Installation designProspective fault current estimate

I_{f} = \frac{U}{Z_{loop}}

Installation designAdiabatic protective conductor calculation

S \geq \frac{\sqrt{I^{2} t}}{k}

Installation designProtective-device let-through energy

I^{2} t \leq k^{2} S^{2}

Installation designTT resistance and residual-current relationship

R_{A} \times I_{Δ n} \leq U_{L}

Installation designMaximum demand with an agreed coincidence factor

I_{demand} = Σ (I_{group} \times f_{group})

Testing and verification

Testing and verificationCalculated earth fault loop impedance

Z_{s} \approx Z_{e} + (R_{1} + R_{2})

Testing and verificationRadial line and CPC resistance

R_{1} + R_{2} = \frac{(r_{1} + r_{2}) L}{1000}

Testing and verificationRing continuity: equal line and neutral

R_{cross} = \frac{r_{1} + r_{n}}{4}

Energy systems

Energy systemsBattery nominal and usable energy

E_{usable} \approx V_{nom} \times Q \times f_{usable}

Energy systemsEstimated battery-backed runtime

t \approx \frac{E_{DC} \times η}{P_{load}}

Energy systemsConversion efficiency and losses

P_{loss} = P_{out} (\frac{1}{η} - 1)

Electrical calculators. 94 tools for everyday electrical maths.

Foundations

Power and energy

Circuits and conductors

Capacitance and inductance

AC foundations

Magnetism

AC power

Motors and transformers

Lighting

Installation design

Testing and verification

Energy systems

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