Formula solver index — formula.expert

Ohm's Law

V = I R

Electricity & MagnetismPhysicsRelates the voltage across a conductor to the current through it and its resistance.

Electrical Power (P = VI)

P = V I

Electricity & MagnetismPhysicsPower delivered to a component as the product of the voltage across it and the current through it.

Electrical Power (P = I²R)

P = I^{2} R

Electricity & MagnetismPhysicsPower dissipated as heat in a resistance carrying a current (Joule heating).

Electrical Power (P = V²/R)

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

Electricity & MagnetismPhysicsPower dissipated in a resistance held at a fixed voltage.

Two Resistors in Series

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

Electricity & MagnetismPhysicsTotal resistance of two resistors connected end to end is simply their sum.

Two Resistors in Parallel

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

Electricity & MagnetismPhysicsTotal resistance of two resistors connected side by side: product over sum, always less than either branch.

Electric Charge (Q = It)

Q = I t

Electricity & MagnetismPhysicsTotal charge transferred by a steady current flowing for a given time.

RC Time Constant

\tau = R C

Electricity & MagnetismPhysicsCharacteristic charging/discharging time of a resistor-capacitor circuit.

RC Capacitor Discharge

V = V_{0} \, e^{-t/\tau}

Electricity & MagnetismPhysicsExponential decay of the voltage on a capacitor discharging through a resistor.

Electrical Energy (E = Pt)

E = P t

Electricity & MagnetismPhysicsEnergy consumed by a device drawing constant power over a period of time.

Coulomb's Law

F = \frac{k_e \, q_{1} q_{2}}{r^{2}}

Electricity & MagnetismPhysicsElectrostatic force between two point charges, with kₑ = 8.9875517923×10⁹ N·m²/C².

Capacitance (C = Q/V)

C = \frac{Q}{V}

Electricity & MagnetismPhysicsDefines capacitance as the charge stored per volt applied across a capacitor.

Energy Stored in a Capacitor

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

Electricity & MagnetismPhysicsEnergy banked in a capacitor's electric field from its capacitance and voltage.

Transformer Voltage Ratio

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

Electricity & MagnetismPhysicsRelates the primary and secondary voltages of an ideal transformer to its turns ratio.

Magnetic Force on a Moving Charge

F = q v B \sin\theta

Electricity & MagnetismPhysicsMagnitude of the magnetic (Lorentz) force on a charge moving through a magnetic field.

Magnetic Force on a Current-Carrying Wire

F = B I L \sin\theta

Electricity & MagnetismPhysicsMagnitude of the force on a straight current-carrying wire in a uniform magnetic field.

Two Capacitors in Series

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

Electricity & MagnetismPhysicsCombines two series capacitors into a total that is smaller than either one.

Two Capacitors in Parallel

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

Electricity & MagnetismPhysicsCombines two parallel capacitors by simply adding their capacitances.

Magnetic Flux (Φ = BA cos θ)

\Phi = B A \cos\theta

Electricity & MagnetismPhysicsThe magnetic field threading a surface: field times area times the cosine of the tilt angle.

Faraday's Law of Induction

\varepsilon = N \frac{\Delta\Phi}{\Delta t}

Electricity & MagnetismPhysicsThe EMF induced in a coil of N turns by flux changing at ΔΦ/Δt (magnitude form).

Motional EMF (ε = BLv)

\varepsilon = B L v

Electricity & MagnetismPhysicsVoltage generated across a conductor of length L moving at speed v through a field B.

Magnetic Field of a Solenoid

B = \frac{\mu_0 N I}{L}

Electricity & MagnetismPhysicsThe uniform field inside a long coil of N turns and length L carrying current I.

Energy Stored in an Inductor

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

Electricity & MagnetismPhysicsEnergy held in an inductor's magnetic field: half the inductance times current squared.

Inductive Reactance (X_L = 2πfL)

X_L = 2\pi f L

Electricity & MagnetismPhysicsAn inductor's opposition to AC current, rising in proportion to frequency.

Capacitive Reactance (X_C = 1/2πfC)

X_C = \frac{1}{2\pi f C}

Electricity & MagnetismPhysicsA capacitor's opposition to AC current, falling as frequency rises.

RL Time Constant (τ = L/R)

\tau = \frac{L}{R}

Electricity & MagnetismPhysicsHow quickly current builds or decays in an inductor-resistor circuit.

LC Resonant Frequency

f = \frac{1}{2\pi\sqrt{LC}}

Electricity & MagnetismWaves & OscillationsPhysicsThe natural oscillation frequency of an inductor-capacitor pair.

RMS and Peak Voltage

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

Electricity & MagnetismPhysicsFor a sine wave, the effective (heating-equivalent) voltage is the peak divided by √2.

Resistance of a Wire (R = ρL/A)

R = \frac{\rho L}{A}

Electricity & MagnetismPhysicsResistance from material resistivity, length, and cross-sectional area.

Force Between Parallel Wires

F = \frac{\mu_0 I_1 I_2 \ell}{2\pi d}

Electricity & MagnetismPhysicsMagnetic force between two parallel current-carrying wires separated by distance d.

Three-Phase Real Power

P = \sqrt{3} \, V_{L} I_{L} \, \text{PF}

Electrical TradeElectricity & MagnetismReal power drawn by a balanced three-phase load from its line-to-line voltage, line current, and power factor.

Single-Phase Real Power with Power Factor

P = V I \, \text{PF}

Electrical TradeElectricity & MagnetismTrue power of a single-phase AC load: volts times amps times power factor, the fraction of the current doing real work.

Three-Phase Apparent Power

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

Electrical TradeElectricity & MagnetismApparent power in volt-amperes for a balanced three-phase load — the quantity that sizes transformers, cables and breakers.

Power Factor from Real and Apparent Power

\text{PF} = \frac{P}{S}

Electrical TradeElectricity & MagnetismPower factor as the ratio of real power in watts to apparent power in volt-amperes, the share of supplied capacity doing work.

Reactive Power (Power Triangle)

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

Electrical TradeElectricity & MagnetismReactive power in vars from the power triangle, where apparent power is the hypotenuse over real and reactive legs.

Power-Factor Correction kvar

Q_{c} = P \left( \tan\varphi_{1} - \tan\varphi_{2} \right)

Electrical TradeElectricity & MagnetismSize of the capacitor bank in vars needed to lift a load from its existing power factor up to a chosen target power factor.

Power-Factor Correction Capacitance

C = \frac{Q_{c}}{2\pi f V^{2}}

Electrical TradeElectricity & MagnetismCapacitance needed across a single-phase load to supply a given number of vars at the supply voltage and frequency.

Phase Angle from Power Factor

\varphi = \arccos(\text{PF})

Electrical TradeElectricity & MagnetismThe angle by which current lags or leads voltage, found from the power factor — the link between the ratio and the triangle.

Wye Line and Phase Voltage

V_{L} = \sqrt{3} \, V_{\varphi}

Electrical TradeElectricity & MagnetismIn a wye (star) connection the line-to-line voltage is √3 times the line-to-neutral phase voltage of each winding.

Delta Line and Phase Current

I_{L} = \sqrt{3} \, I_{\varphi}

Electrical TradeElectricity & MagnetismIn a delta connection the line current is √3 times the current in each winding, while line and phase voltages are equal.

Voltage Drop, Single Phase

V_{d} = \frac{2 \rho L I}{A}

Electrical TradeElectricity & MagnetismVoltage lost in a single-phase run from conductor resistivity, one-way length, current and area — the 2 counts both conductors.

Voltage Drop, Three Phase

V_{d} = \frac{\sqrt{3} \, \rho L I}{A}

Electrical TradeElectricity & MagnetismLine-to-line voltage drop on a balanced three-phase run, using √3 rather than 2 because there is no return conductor.

Percent Voltage Drop

\%V_{d} = \frac{100 \, V_{d}}{V_{s}}

Electrical TradeElectricity & MagnetismVoltage drop expressed as a percentage of the supply voltage, the form codes use for the 3% branch and 5% total limits.

Three-Phase Motor Full-Load Current

I = \frac{P_{out}}{\sqrt{3} \, V \, \text{PF} \, \eta}

Electrical TradeElectricity & MagnetismLine current of a three-phase motor from its shaft output power, voltage, power factor and nameplate efficiency in percent.

Motor Efficiency

\eta = \frac{100 \, P_{out}}{P_{in}}

Electrical TradeElectricity & MagnetismPercentage efficiency of a motor or drive as mechanical output power divided by electrical input power, times one hundred.

Induction Motor Slip

s = \frac{100 \, (N_{s} - N_{r})}{N_{s}}

Electrical TradeElectricity & MagnetismPercent slip of an induction motor: how far the rotor falls behind the rotating magnetic field, as a share of synchronous speed.

Synchronous Speed from Frequency and Poles

N_{s} = \frac{2f}{p}

Electrical TradeElectricity & MagnetismSpeed of an AC machine's rotating field from supply frequency and pole count — the familiar 120f/p when read out in rpm.

Conductor Resistance Temperature Correction

R_{2} = R_{1} \left[ 1 + \alpha (T_{2} - T_{1}) \right]

Electrical TradeElectricity & MagnetismCorrects a conductor's resistance from one temperature to another using the material's temperature coefficient of resistance.

Voltage Divider

V_{out} = V_{in} \frac{R_{2}}{R_{1} + R_{2}}

Electrical TradeElectricity & MagnetismOutput of two resistors in series across a source: the input voltage split in proportion to the lower resistor's share.

Current Divider

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

Electrical TradeElectricity & MagnetismHow a total current splits between two parallel resistors — each branch takes the share set by the opposite resistance.

Series RLC Impedance

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

Electrical TradeElectricity & MagnetismMagnitude of impedance in a series RLC circuit, combining resistance with the net reactance left after XL and XC cancel.

Series RL or RC Impedance

Z = \sqrt{R^{2} + X^{2}}

Electrical TradeElectricity & MagnetismImpedance magnitude of a resistance in series with a single reactance, whether that reactance is inductive or capacitive.

Q Factor of a Series Resonant Circuit

Q = \frac{1}{R} \sqrt{\frac{L}{C}}

Electrical TradeElectricity & MagnetismQuality factor of a series RLC circuit, measuring how sharply it resonates and how much it magnifies voltage at resonance.

Decibel Power Gain

G_{dB} = 10 \log_{10}\!\left(\frac{P_{2}}{P_{1}}\right)

Electrical TradeElectricity & MagnetismGain or loss in decibels between two power levels, the logarithmic ratio used throughout audio, RF and communications work.

Decibel Voltage Gain

G_{dB} = 20 \log_{10}\!\left(\frac{V_{2}}{V_{1}}\right)

Electrical TradeElectricity & MagnetismGain or loss in decibels computed from a voltage ratio, which carries a factor of 20 because power varies with the square of voltage.

LED Series Resistor

R = \frac{V_{s} - V_{f}}{I}

Electrical TradeElectricity & MagnetismResistor needed to run an LED at a chosen current from a given supply, absorbing the difference above the forward voltage.

Inverting Op-Amp Gain

G = -\frac{R_{f}}{R_{in}}

Electrical TradeElectricity & MagnetismClosed-loop gain of an inverting operational amplifier, set purely by the ratio of feedback resistor to input resistor.

Non-Inverting Op-Amp Gain

G = 1 + \frac{R_{f}}{R_{in}}

Electrical TradeElectricity & MagnetismClosed-loop gain of a non-inverting operational amplifier, always one more than the feedback-to-ground resistor ratio.

555 Astable Frequency

f = \frac{1}{\ln 2 \, (R_{1} + 2R_{2}) C}

Electrical TradeElectricity & MagnetismOutput frequency of a 555 timer in astable mode; datasheets round the exact 1/ln2 factor in the numerator to 1.44.