What is the formula for voltage?

Three different formulas, depending on what you know. Ohm's Law: V = I·R (current × resistance). Voltage drop in a wire: Vdrop = 2·L·I·ρ/A (length, current, resistivity, area). Power form: V = P/I or V = √(P·R). For a 0.5 A current through a 100 Ω resistor: V = 0.5 × 100 = 50 V. The calculator above (Voltage Drop) handles the most common practical case — voltage lost along a conductor run.

How do you calculate voltage in a circuit?

For a single resistor or load with known current and resistance: V = I·R (Ohm's Law). For voltage at a load downstream of a wire run: Vload = Vsource − Vdrop, where Vdrop = 2·L·I·ρ/A. For a series circuit, voltages add up to the source: Vsource = V1 + V2 + ... + Vn (Kirchhoff). For parallel branches, voltage across each branch equals the source voltage; currents divide instead.

What is DC voltage versus AC voltage?

DC (direct current) voltage is constant in time — battery, solar panel, USB power. The voltage value is just the steady level. AC (alternating current) voltage oscillates, typically as a sine wave — mains power, alternator output. AC voltage is usually quoted as RMS (root-mean-square): the equivalent DC voltage that delivers the same average power. For a sinusoidal wave: Vrms = Vpeak/√2 ≈ 0.707·Vpeak. So 120 V AC mains has a peak of about 170 V; 240 V AC has a peak of about 339 V.

What is considered low, medium, and high voltage?

Definitions per IEC 60038 + IEEE 1585: Low voltage ≤ 1000 V AC (≤ 1500 V DC) — covers residential 120/240 V, commercial 480 V, industrial 600 V. Medium voltage 1–35 kV — distribution feeders, industrial substations, utility primary. High voltage 35–230 kV — sub-transmission. Extra-high voltage > 230 kV — transmission lines. NEC uses slightly different thresholds: ≤ 600 V is low for most articles, > 600 V triggers Article 490 ("Equipment over 1000 V").

How many millivolts in a volt?

1 V = 1000 mV. The full SI prefix ladder for voltage: 1 kV (kilovolt) = 1000 V; 1 V (volt) = 1000 mV (millivolt) = 1 000 000 µV (microvolt). Used commonly: 5 V → 5000 mV; 24 V battery → 24 000 mV; 120 V mains → 120 000 mV. In RF and small-signal electronics, voltages of a few millivolts (sensor signals, thermocouple outputs) are amplified to volt-level for processing.

What is terminal voltage versus EMF?

EMF (electromotive force) ε is the open-circuit voltage of a source — battery or generator with no load connected. Terminal voltage Vterminal is what you measure across the source's terminals when a load draws current; it is always less than EMF because the source's internal resistance r drops some voltage internally: Vterminal = ε − I·r. A car battery rated 12.6 V (EMF) might show 11.8 V (terminal) under cranking load — that 0.8 V difference is the I·r drop across the internal cell resistance.

How do you reduce voltage in a circuit?

Four common methods. (1) Voltage divider with two resistors: Vout = Vin · R2/(R1+R2) — wasteful, only for low-current signal level shifting. (2) Linear regulator (LM7805 etc.) — clean output but burns the difference as heat, efficiency = Vout/Vin. (3) Switch-mode (DC-DC) converter — high efficiency (85–95%), the practical choice for power applications. (4) Transformer for AC — passive, very efficient, ratio set by turns. Picking depends on the input/output voltage difference, current, and efficiency requirement.

How to reduce voltage in a circuit?

Same answer as above — picking from voltage divider, linear regulator, switch-mode DC-DC converter, or transformer based on the input voltage, output voltage, current, and efficiency target.

How to figure out voltage?

Three quick paths to figure out voltage in a circuit. (1) From current and resistance via Ohm's Law: V = I × R. (2) From power and current: V = P / I. (3) From the source voltage minus the conductor drop: V_load = V_source − V_drop, where V_drop = 2 · L · I · ρ / A. The voltage drop calculator above does the third — the most common engineering case.

On a real circuit you "get" voltage in one of three ways. (1) Direct measurement with a multimeter or oscilloscope — the meter probes go between the two points whose potential difference you want. (2) Compute from Ohm's Law if you know current and resistance. (3) Read the source nameplate (battery, supply, transformer secondary) — for an unloaded source this is the open-circuit voltage; under load it sags by I × r_internal.

How many mV in a volt?

How many mV in a volt: 1 V = 1 000 mV. The full ladder of voltage SI prefixes: 1 kV = 1 000 V; 1 V = 1 000 mV (millivolt); 1 mV = 1 000 µV (microvolt). A 5 V USB rail is 5 000 mV, a 24 V battery is 24 000 mV, and a thermocouple output of 41 mV at 1 000 °C is 0.041 V.

What is A/C voltage (also written as a c voltage): the voltage of an alternating-current source whose polarity reverses periodically. Mains AC in North America is nominally 120 V at 60 Hz; in Europe it is 230 V at 50 Hz; industrial three-phase is 400 V (EU) or 480 V (US). The number quoted for AC voltage is always the RMS value (V_rms = V_peak / √2 for a pure sine).

What is considered medium voltage?

What is considered medium voltage: per IEEE 1585 and IEC 60038, medium voltage is the range from 1 kV to 35 kV (also called the medium voltage range). Common distribution-class values inside this band are 4.16 kV, 13.8 kV, 25 kV, and 35 kV. Below 1 kV is low voltage; above 35 kV is high voltage and then extra-high voltage above 230 kV.

Calculator · Electrical · DC + AC · LV / MV / HV

Voltage

Voltage formulas, conversions, classifications, and a working voltage calculator. Ohm\'s Law for the simple case, the voltage loss formula for real conductor runs, AC RMS and three-phase line-to-line for power systems. Built around the engineer\'s practical question: how much voltage actually reaches the load?

Use the voltage drop calculator

The most common voltage calculation in electrical practice is voltage drop along a conductor run. Below is the same calculator featured on the dedicated Voltage Drop Calculator page — DC, single-phase AC, and three-phase modes; copper or aluminium; AWG or mm² standard sizes; NEC 3% / 5% compliance check.

CALC.001 Voltage Drop · Cu/Al · DC + 1Φ + 3Φ

Material[Mat]

Size standard[Std]

Conductor size[A]

Current[I]

Length one-way[L]

System voltage[V]

Conductor temperature[T]

°C

Voltage drop · V_drop

— V

0510%

Drop ratio: —
V at load: —
Power loss: —
ρ used (T-corrected): —

FORMULA · V = 2 · L · I · ρ / A NEC 3% / 5% RULE

The voltage formula, in four practical forms

Voltage rarely needs just one formula. Different engineering contexts call for different forms — circuit analysis uses Ohm\'s Law, conductor sizing uses the voltage loss formula (also written as the drop voltage formula or drop voltage calculation formula), AC power systems use RMS and the three-phase line-to-line relationship. The same set of equations covers the power and voltage formula combinations every engineer reaches for.

Eq. 01 — Ohm's Law (single resistor or component) SI · Ohm 1827

V = I \cdot R

V: voltage across the component, V
I: current through it, A
R: resistance, Ω

Eq. 02 — Voltage drop along a conductor (DC and 1-phase AC) SI · NEC Table 9 · IEC 60287

V_{drop} = \frac{2 \cdot L \cdot I \cdot \rho}{A}

V_drop: voltage lost along the wire run, V
L: one-way conductor length, m
I: load current, A
ρ: resistivity (Cu 0.0175, Al 0.028 at 20°C), Ω·mm²/m
A: cross-sectional area, mm²

Eq. 03 — AC RMS to peak (sinusoidal) SI · IEEE / Standard textbook

V_{rms} = \frac{V_{peak}}{\sqrt{2}} \approx 0.707 \cdot V_{peak}

V_rms: root-mean-square voltage (the value your meter shows on AC), V
V_peak: instantaneous peak of the sine wave, V

Eq. 04 — Three-phase line-to-line vs phase voltage (Y configuration) SI · IEEE Power System Engineering

V_{LL} = \sqrt{3} \cdot V_{phase}

V_LL: line-to-line voltage (between any two phases), V
V_phase: line-to-neutral voltage (single-phase reading), V

For example: a 400 V three-phase Y system has a phase voltage of 400 / √3 ≈ 231 V, which is what a single-phase load between line and neutral sees. The familiar 230 V European mains and 400 V three-phase grids are the same system viewed from these two perspectives.

Worked example: voltage at a load 30 m from a 240 V source

A 20 A heater on a 240 V single-phase circuit, supplied through 30 m of 10 AWG copper (5.26 mm²). What voltage actually reaches the heater?

Step	Calculation	Result
Source voltage	given	240 V
Resistivity ρ_Cu at 20°C	NEC Table 8	0.0175 Ω·mm²/m
Voltage drop	V_drop = 2 × 30 × 20 × 0.0175 / 5.26	3.99 V
Drop ratio	3.99 / 240 × 100%	1.66%
NEC compliance	1.66% ≤ 3% branch limit	PASS
Voltage at heater	V_load = 240 − 3.99	236.01 V
Equivalent at 12 V DC system	same drop, V_load = 12 − 3.99	8.01 V (33% drop — fails)

The 4 V drop is acceptable on 240 V mains but catastrophic on 12 V DC — the same absolute drop is a different percentage of the source. This is why low-voltage DC installations (RV, marine, solar) need much larger wires than mains-voltage AC for the same current and length.

Voltage compared to current, resistance, and power

Voltage is one of four primary electrical quantities that an engineer sizes against, all related through Ohm\'s Law and the power equation P = V·I.

Quantity	Symbol	Unit	What it represents	Where it controls design
Voltage	V	volt (V)	electrical "pressure" between two points	insulation rating, system design (LV/MV/HV)
Current	I	ampere (A)	flow of electric charge per second	conductor sizing (ampacity), breaker rating
Resistance	R	ohm (Ω)	opposition to current flow	component selection, voltage drop
Power	P	watt (W)	rate of energy transfer (P = V·I)	equipment rating, energy consumption

Engineers think in different units depending on the problem: service entrance sized in amps, insulation rated in kV, equipment labelled in watts or HP, circuit analysis done in volts and ohms. The four quantities relate through V = I·R and P = V·I; pick the form that matches what you know.

Variants and special cases

DC voltage

Constant in time. Source examples: batteries (12 V car, 24 V truck, 48 V telecom, 1.5 V cell, 3.7 V lithium), solar panels (typically 24 V or 48 V at maximum power point), DC bus rails in industrial automation. DC voltage is straightforward to measure (any multimeter) and analyse (Ohm\'s Law works directly). The downside is that DC cannot be efficiently transformed up or down at scale — historically the reason AC won the "war of currents" for distribution.

AC voltage and RMS

Alternating current voltage is a sine wave (or close to it for power-system AC). Three relevant numbers: peak (the maximum instantaneous value), peak-to-peak (twice the peak), and RMS (the equivalent DC voltage delivering the same average power). When someone says "120 V AC", they always mean RMS unless explicitly stated. RMS = peak / √2 for any pure sinusoid; for distorted waveforms (chopper-driven loads, harmonics), RMS must be measured with a true-RMS meter.

Phase voltage and line-to-line voltage

In a three-phase system, "phase voltage" is between any single phase and neutral, while "line-to-line" (or just "line") voltage is between any two phases. For a star (Y) configuration: V_LL = √3 · V_phase. So a 400/230 V system has 400 V line-to-line and 230 V line-to-neutral — both are correct depending on what you measure between. A single-phase load on three-phase service is connected line-to-neutral and sees phase voltage; a three-phase motor connects line-to-line.

Low voltage (LV)

Per IEC 60038 / IEEE 1585: ≤ 1000 V AC or ≤ 1500 V DC. Covers all residential (120 V US, 230 V EU), commercial (480 V US, 400 V EU), and most industrial systems below 1 kV. NEC uses ≤ 600 V as its primary low-voltage threshold for the bulk of the code — Article 490 kicks in above 1000 V.

Medium voltage (MV)

1 kV to 35 kV per IEEE 1585. Distribution-class voltages: 4.16 kV, 13.8 kV, 25 kV, 35 kV. Used for utility distribution feeders and large industrial primary. Requires special equipment ratings, clearance distances, and dedicated MV switchgear. NEC Article 490 covers MV practice in the US.

High voltage (HV) and extra-high voltage (EHV)

HV: 35–230 kV (sub-transmission). EHV: > 230 kV (transmission). HV/EHV is the realm of utility transmission engineers — overhead lines, substations, sectionalizing switches. Outside the scope of NEC but covered by IEEE C2 (National Electrical Safety Code).

Voltage range and regulation

Real systems do not deliver exactly nominal voltage — they vary with load and time. Voltage regulation = (V_noload − V_fullload) / V_fullload, expressed as a percentage. ANSI C84.1 defines acceptable service voltage ranges: ±5% Range A (normal operation), ±5.8 to −13.3% Range B (occasional excursions). Equipment is designed for these ranges; outside them performance degrades or trip-outs occur.

Neutral voltage

In a balanced three-phase Y-connected system, the neutral conductor carries near-zero current and sits at near-zero voltage relative to ground. Imbalance (uneven loading on the three phases) shifts the neutral and produces "neutral-to-ground voltage", typically ≤ 2 V in well-balanced systems and a sign of trouble (heavy single-phase load on one leg, harmonics) above 5 V.

Terminal voltage versus EMF

Battery and generator data sheets quote two voltages: open-circuit (EMF) and terminal at rated load. Terminal voltage = EMF − I·r_internal. For a 12 V car battery with 0.02 Ω internal resistance carrying 200 A starter current: terminal V = 12.6 − 200 × 0.02 = 8.6 V — the dramatic dip everyone notices when cranking. As internal resistance grows with age or cold, the dip deepens; eventually the cranking voltage drops below the starter\'s threshold and the engine refuses to turn.

Voltage in series circuits

Kirchhoff\'s voltage law: around any closed loop, the sum of all voltage rises equals the sum of all drops. For a single source feeding several resistors in series: V_source = V_R1 + V_R2 + ... + V_Rn, with the same current flowing through every resistor. See the Calculate Voltage Drop tutorial for a worked series-circuit example.

Voltage in parallel circuits

For elements in parallel, voltage across each branch is the same and equal to the source. Currents divide between branches in inverse proportion to their resistance: I_i = V/R_i. Used in residential wiring (every outlet sees mains voltage; loads draw their share of current), in capacitor banks for power-factor correction, and anywhere multiple loads share a bus.

Voltage divider

Two resistors in series with output taken at the midpoint: V_out = V_in · R₂/(R₁+R₂). Common in low-current sensor and reference circuits. Loaded voltage dividers (with a load drawing current from V_out) sag under load — for any meaningful current draw, use a regulator or buffer instead of a raw divider.

Voltage quick reference

Topic	Quick answer
Power and voltage formula	P = V × I (DC); P = V × I × cos φ (1-φ AC); P = √3 × V_LL × I × cos φ (3-φ AC). The same set of relationships goes in reverse: power voltage and voltage power conversions both come from rearranging P = V × I.
Voltage for 3 phase	Common nominal 3-phase voltages: 208 V, 240 V, 400 V (EU), 415 V (UK), 480 V (US), 600 V (Canada). Voltage for 3 phase is always quoted line-to-line unless explicitly written line-to-neutral.
Three phase voltage drop formula / 3 phase voltage drop formula	V_drop = √3 × I × (R_eff cos φ + X_eff sin φ) × L / 1000, with R_eff and X_eff in Ω/km from cable tables. Single-phase uses the factor 2 instead of √3.
Phase vs line voltage	Line voltage (V_LL) is between two phases; phase voltage (V_LN) is between one phase and neutral. For Y systems V_LL = √3 × V_LN; for Δ systems V_LL = V_phase.
230 volt	European household nominal (EU/UK harmonised at 230 V ± 10 %, single-phase, 50 Hz). Equivalent to the line-to-neutral value of a 400 V three-phase Y system.
Medium voltage range	1 kV to 35 kV per IEEE 1585 — the same band described in the Medium Voltage variant above.
Max voltage	The highest voltage allowed on a circuit before insulation or clearance is exceeded. NEC examples: 600 V class building wire is rated to 600 V max nominal; 1 000 V is the LV / MV boundary; transmission EHV runs to 765 kV in the US (UHV up to 1.1 MV).
Outlet low voltage	Low-voltage receptacle outlets (12 V or 24 V landscape, 24 V doorbell, 12 V auto) are NEC Class 2 / Class 3 power-limited circuits with reduced shock and fire risk. Wired with bell wire (18–22 AWG).
Rating voltage	The voltage at which a component is designed to operate continuously without insulation failure. Capacitors, motors, transformers, and conductors all carry a rating voltage on the nameplate — for safety always pick a part with rating voltage ≥ the highest expected circuit voltage including transients.
VDC voltage	VDC = "volts direct current" — used to distinguish DC measurements from VAC (volts alternating current). A "12 VDC supply" means 12 V steady, regardless of polarity reversals.
Dr voltage	"Dr voltage" is a common search misspelling of "drop voltage". The drop voltage formula and drop voltage calculation formula are the same as the voltage loss formula in Eq. 02 above.
Voltage loss chart	A voltage loss chart maps conductor cross-section to allowable run length for a given current at a given % drop. NEC tables give 3 % branch / 5 % feeder limits; AS/NZS 3008 gives equivalent metric tables.
Calculator voltage / voltamp calculator	The "calculator voltage" and "voltamp calculator" use cases are covered by the embedded Voltage Drop Calculator above. For full V·I·R·P conversions see /power/.
DC voltage wire size calculator / wire size calculator dc voltage / dc voltage loss calculator / dc power voltage drop calculator	For DC sizing — common in solar, RV, marine, and 12/24/48 V battery work — use the voltage drop calculator set to DC mode. The same V_drop = 2 · L · I · ρ / A formula governs; only the RMS / power-factor terms drop out.

Related concepts on this site

Frequently asked questions

What is the formula for voltage?: Three different formulas, depending on what you know. Ohm's Law: V = I·R (current × resistance). Voltage drop in a wire: V_drop = 2·L·I·ρ/A (length, current, resistivity, area). Power form: V = P/I or V = √(P·R). For a 0.5 A current through a 100 Ω resistor: V = 0.5 × 100 = 50 V. The calculator above (Voltage Drop) handles the most common practical case — voltage lost along a conductor run.
How do you calculate voltage in a circuit?: For a single resistor or load with known current and resistance: V = I·R (Ohm's Law). For voltage at a load downstream of a wire run: V_load = V_source − V_drop, where V_drop = 2·L·I·ρ/A. For a series circuit, voltages add up to the source: V_source = V₁ + V₂ + ... + V_n (Kirchhoff). For parallel branches, voltage across each branch equals the source voltage; currents divide instead.
What is DC voltage versus AC voltage?: DC (direct current) voltage is constant in time — battery, solar panel, USB power. The voltage value is just the steady level. AC (alternating current) voltage oscillates, typically as a sine wave — mains power, alternator output. AC voltage is usually quoted as RMS (root-mean-square): the equivalent DC voltage that delivers the same average power. For a sinusoidal wave: V_rms = V_peak/√2 ≈ 0.707·V_peak. So 120 V AC mains has a peak of about 170 V; 240 V AC has a peak of about 339 V.
What is considered low, medium, and high voltage?: Definitions per IEC 60038 + IEEE 1585: Low voltage ≤ 1000 V AC (≤ 1500 V DC) — covers residential 120/240 V, commercial 480 V, industrial 600 V. Medium voltage 1–35 kV — distribution feeders, industrial substations, utility primary. High voltage 35–230 kV — sub-transmission. Extra-high voltage > 230 kV — transmission lines. NEC uses slightly different thresholds: ≤ 600 V is low for most articles, > 600 V triggers Article 490 ("Equipment over 1000 V").
How many millivolts in a volt?: 1 V = 1000 mV. The full SI prefix ladder for voltage: 1 kV (kilovolt) = 1000 V; 1 V (volt) = 1000 mV (millivolt) = 1 000 000 µV (microvolt). Used commonly: 5 V → 5000 mV; 24 V battery → 24 000 mV; 120 V mains → 120 000 mV. In RF and small-signal electronics, voltages of a few millivolts (sensor signals, thermocouple outputs) are amplified to volt-level for processing.
What is terminal voltage versus EMF?: EMF (electromotive force) ε is the open-circuit voltage of a source — battery or generator with no load connected. Terminal voltage V_terminal is what you measure across the source's terminals when a load draws current; it is always less than EMF because the source's internal resistance r drops some voltage internally: V_terminal = ε − I·r. A car battery rated 12.6 V (EMF) might show 11.8 V (terminal) under cranking load — that 0.8 V difference is the I·r drop across the internal cell resistance.
How do you reduce voltage in a circuit?: Four common methods. (1) Voltage divider with two resistors: V_out = V_in · R₂/(R₁+R₂) — wasteful, only for low-current signal level shifting. (2) Linear regulator (LM7805 etc.) — clean output but burns the difference as heat, efficiency = V_out/V_in. (3) Switch-mode (DC-DC) converter — high efficiency (85–95%), the practical choice for power applications. (4) Transformer for AC — passive, very efficient, ratio set by turns. Picking depends on the input/output voltage difference, current, and efficiency requirement.
How to reduce voltage in a circuit?: Same answer as above — picking from voltage divider, linear regulator, switch-mode DC-DC converter, or transformer based on the input voltage, output voltage, current, and efficiency target.
How to figure out voltage?: Three quick paths to figure out voltage in a circuit. (1) From current and resistance via Ohm's Law: V = I × R. (2) From power and current: V = P / I. (3) From the source voltage minus the conductor drop: V_load = V_source − V_drop, where V_drop = 2 · L · I · ρ / A. The voltage drop calculator above does the third — the most common engineering case.
How to get voltage?: On a real circuit you "get" voltage in one of three ways. (1) Direct measurement with a multimeter or oscilloscope — the meter probes go between the two points whose potential difference you want. (2) Compute from Ohm's Law if you know current and resistance. (3) Read the source nameplate (battery, supply, transformer secondary) — for an unloaded source this is the open-circuit voltage; under load it sags by I × r_internal.
How many mV in a volt?: How many mV in a volt: 1 V = 1 000 mV. The full ladder of voltage SI prefixes: 1 kV = 1 000 V; 1 V = 1 000 mV (millivolt); 1 mV = 1 000 µV (microvolt). A 5 V USB rail is 5 000 mV, a 24 V battery is 24 000 mV, and a thermocouple output of 41 mV at 1 000 °C is 0.041 V.
What is A/C voltage?: What is A/C voltage (also written as a c voltage): the voltage of an alternating-current source whose polarity reverses periodically. Mains AC in North America is nominally 120 V at 60 Hz; in Europe it is 230 V at 50 Hz; industrial three-phase is 400 V (EU) or 480 V (US). The number quoted for AC voltage is always the RMS value (V_rms = V_peak / √2 for a pure sine).
What is considered medium voltage?: What is considered medium voltage: per IEEE 1585 and IEC 60038, medium voltage is the range from 1 kV to 35 kV (also called the medium voltage range). Common distribution-class values inside this band are 4.16 kV, 13.8 kV, 25 kV, and 35 kV. Below 1 kV is low voltage; above 35 kV is high voltage and then extra-high voltage above 230 kV.

Sources and methodology

NFPA. National Electrical Code (NEC) NFPA 70, 2023 Edition. Article 100 (definitions), Article 210.19(A) (voltage drop), Article 490 (over 1000 V).
IEC. IEC 60038:2009 — IEC Standard Voltages. Standard nominal voltages for AC and DC systems worldwide.
IEEE. IEEE Std 1585-2002 — Guide for the Functional Specification of Medium-Voltage Apparatus. Voltage classification thresholds.
ANSI. ANSI C84.1-2020 — Electric Power Systems and Equipment, Voltage Ratings (60 Hz). Voltage range A and B definitions.
Ohm, G. S. Die galvanische Kette, mathematisch bearbeitet, 1827. Original statement of V = I·R.
Kirchhoff, G. R. Ueber den Durchgang eines elektrischen Stromes durch eine Ebene, Annalen der Physik, 1845. Voltage and current laws.