How to calculate power from voltage and current?

For DC or resistive AC: P (W) = V (volts) × I (amps). For single-phase AC with reactive load: P = V × I × cos φ where cos φ is power factor (typically 0.85–0.95 for motors). For three-phase AC: P = √3 × V_LL × I × cos φ. A 480 V × 50 A 3-φ motor at PF 0.9: P = 1.732 × 480 × 50 × 0.9 = 37 411 W ≈ 37.4 kW.

How to calculate power using voltage and current?

Same as the previous formula — P = V × I × PF for AC, P = V × I for DC. The "current voltage power formula" is the foundation of the V-I-P-R triangle: any one of the four (V, I, P, R) can be derived from any two of the others using Ohm's law (V = I × R) and Joule's law (P = V × I = I² × R = V² / R). For AC, multiply by power factor.

How to find resistance with voltage and current?

R = V / I (Ohm's law, rearranged). A 12 V battery driving 0.5 A through a load: R = 12 / 0.5 = 24 Ω. For AC circuits with reactive components, what you actually compute is impedance Z, not pure resistance: |Z| = V / I (magnitude); to separate R and X you need a phase measurement. For DC and purely resistive AC, R = V / I is exact.

How to calculate resistance with voltage and current?

Identical answer: R = V / I. A 240 V circuit drawing 8 A through a heater coil: R = 240 / 8 = 30 Ω. The heater element dissipates P = V × I = 240 × 8 = 1 920 W, equivalent to P = V² / R = 240² / 30 = 1 920 W or P = I² × R = 64 × 30 = 1 920 W. All three forms agree (Joule's law).

How to calculate power voltage and current?

Use the V-I-P-R triangle. Given any two of (V, I, P, R), compute the other two. The four canonical equations: V = I × R, P = V × I, P = I² × R, P = V² / R. For AC, multiply current-voltage products by power factor (cos φ). The embedded calculator handles every combination — see /power/ for the full V-I-R-P engine.

How to calculate motor starting current?

Motor starting current (= locked-rotor amperage, LRA) is typically 5–8 × full-load current for an across-the-line started induction motor. NEMA Code Letters A through V (on the nameplate) indicate the locked-rotor kVA per HP at rated voltage: Code G ≈ 5.6, Code H ≈ 6.3, Code J ≈ 7.1, Code K ≈ 8.0. For a 50 HP Code G motor: LRA ≈ 50 × 5.6 × 1000 / (1.732 × 460) = 351 A vs FLA of 65 A — a 5.4 × inrush. Use a soft-starter or VFD to limit inrush.

How to calculate the starting current of a motor?

Same calculation as the previous answer — apply the NEMA Code Letter from the motor nameplate. LRA = (Code Letter kVA / HP) × HP × 1000 / (V_LL × √3) for 3-phase. Or use the rule of thumb: starting current = 6 × FLA for typical NEMA Design B motors. For premium high-efficiency motors (Code F or G), starting current can be up to 8 × FLA — verify with the manufacturer data sheet.

How to calculate starting current of motor?

Identical: I_start ≈ NEMA_code_kVA × HP × 1000 / (V_LL × √3). Use the actual nameplate Code Letter — designs vary. NEMA Design B (most industrial motors): Code G or H, ~ 5.5–6.5 × FLA. NEMA Design D (high-slip, hoist motors): Code A or B, ~ 3 × FLA. NEMA Premium / IE3 / IE4: often higher LRA than older Class B motors due to better magnetic steel.

What is full load current?

Full load current (FLC or FLA) is the steady-state current a motor (or load) draws at its rated horsepower output and rated voltage. For 3-phase induction motors, NEC Table 430.250 lists standardized FLC values that supersede the nameplate for branch-circuit sizing — e.g., 50 HP @ 460 V 3-φ = 65 A FLC per NEC. The table values include some margin above typical nameplate values to ensure conductor and breaker headroom.

What is load current?

Load current is the current actually drawn by a connected load at any moment — varies with applied voltage, load condition, and (for motors) shaft load. Not the same as full-load current: a motor lightly loaded may draw 30 A even though its FLA is 65 A. For sizing protection and conductors, always use the full-load current (or NEC nameplate equivalent), not the measured operating load.

Reference · Electrical · DC · AC · 3-phase · NEC 430.250 · Ohm's law

Current — Calculator, Formulas & Reference

Working reference for the current calculator, with every common formula in one place: current calculation for DC, single-phase, and three-phase AC; three phase current calculation with line-to-line and line-to-neutral; direct current voltage drop calculator integration; alternating current formula with RMS / peak / average relationships; and the wire gauge and current rating from NEC 310.16. Includes motor full-load and starting current per NEC 430.250 and NEMA Code Letters. Reviewed by a licensed PE.

Current calculator — all modes

The embedded current calculator solves for I given V and P, V given I and P, or P given V and I — with switches for DC, single-phase AC (with PF), and three-phase AC (line-to-line + PF). Works as a three phase current calculator, 3 phase current calculator, or alternating current calculator. For an ac to dc current calculator use case, switch the AC side to DC and adjust voltage accordingly (RMS → DC equivalent for resistive loads).

CALC.007 Universal Power · V · I · P · R · 3 modes · 6 solve combos

I know:[Given]

Voltage V[V]

Current I[I]

Power P[P]

Resistance R[R]

Pure DC: P = V · I. Resistance shown is V/I (Ohm's law equivalent).

Voltage V

— V

Current I

— A

Power P

— W

Resistance R

— Ω

Apparent power S: — kVA
Reactive power Q: — kVAR
Power factor used: —
Mechanical equivalent: — HP
Heat output: — BTU/hr

Show your work

P = V · I = ...

FORMULA · P = V · I (DC) SOURCE · OHM 1827 · IEEE STD 100

Current formulas — Ohm's law and AC variants

Eq. 01 — Ohm's law (the universal current formula) SI

I = \frac{V}{R}

·: V in volts, R in ohms; I in amperes.
·: Holds for DC and resistive AC; for reactive AC use impedance Z instead of R.
·: Foundation of all current calculations — every other formula reduces to this with substitution.

Eq. 02 — Single-phase AC current from power SI

I = \frac{P}{V \cdot \cos \varphi}

·: V = RMS voltage, cos φ = displacement power factor.
·: For PF 1.0 (resistive): same as DC. For PF 0.5: doubles the current for the same real power.
·: Conductor must be sized to this current, not the underlying real power.

Eq. 03 — Three-phase AC line current SI

I_L = \frac{P}{\sqrt{3} \cdot V_{LL} \cdot \cos \varphi}

·: V_LL = line-to-line RMS voltage; I_L = line current (= phase current in Y, ≠ in Δ).
·: For 480 V 3-φ at 50 kW PF 0.9: I = 50 000 / (1.732 × 480 × 0.9) = 66.8 A.
·: For unbalanced systems, compute per-phase and use symmetrical components.

Eq. 04 — Motor locked-rotor / starting current SI

I_{start} = K_{NEMA} \cdot HP \cdot \frac{1000}{V_{LL} \cdot \sqrt{3}} \quad (3\text{-}\varphi)

·: K_NEMA = locked-rotor kVA per HP from NEMA Code Letter on nameplate.
·: Code G ≈ 5.6, Code H ≈ 6.3, Code J ≈ 7.1, Code K ≈ 8.0.
·: Typical induction motor: starting current ≈ 5–8 × FLA across-the-line.

Standards governing current calculations

Standard	Scope	Region
NEC / NFPA 70 — Article 430	Motor branch-circuit FLA, starting current, protection	USA
NEC Table 310.16	Conductor ampacity — current carrying capacity by AWG and temperature	USA
NEC Table 430.250	Standardized motor full-load current values (3-phase)	USA
NEMA MG 1 § 10	Code Letter definitions for locked-rotor kVA per HP	USA
IEC 60364	Low-voltage electrical installations — current carrying capacity	Worldwide
BS 7671 Tables 4D1A–4F3A	Conductor current capacity by installation method (UK)	UK

Wire gauge and current rating reference

The wire gauge and current rating table per NEC 310.16 (75 °C copper THWN-2). For 14 awg current rating: 20 A. For current rating 18 awg: not in NEC 310.16 (fixture wire only) — typical 14 A at 90 °C per NEC 402.5.

AWG	Cu 60 °C (A)	Cu 75 °C (A)	Cu 90 °C (A)	Al 75 °C (A)	Standard breaker (A)
14	15	20	25	—	15
12	20	25	30	20	20
10	30	35	40	30	30
8	40	50	55	40	40 / 50
6	55	65	75	50	60
4	70	85	95	65	70 / 80
2	95	115	130	90	100
1/0	125	150	170	120	125 / 150
2/0	145	175	195	135	175 / 200
4/0	195	230	260	180	200 / 225

3 phase motor current chart — NEC Table 430.250

NEC-mandated 3 phase motor current chart values for sizing branch conductors and protection. Use these — not nameplate — per NEC 430.6(A).

HP	208 V (A)	230 V (A)	460 V (A)	575 V (A)
1	4.6	4.2	2.1	1.7
2	7.5	6.8	3.4	2.7
5	16.7	15.2	7.6	6.1
7.5	24.2	22	11	9
10	30.8	28	14	11
15	46.2	42	21	17
20	59.4	54	27	22
25	74.8	68	34	27
30	88	80	40	32
40	114	104	52	41
50	143	130	65	52
75	211	192	96	77
100	273	248	124	99
150	396	360	180	144
200	528	480	240	192

Identify the type of current — DC, single-phase AC, or 3-phase AC. DC: continuous flow in one direction (battery, solar PV before inverter, EV battery pack). Single-phase AC: 60 Hz residential 120 / 240 V (USA) or 50 Hz 230 V (EU/UK). Three-phase AC: industrial 208 / 480 / 600 V — three sinusoids displaced by 120°. The formulas differ by a √3 factor between 1-φ and 3-φ.
Pick the equation by what you know (V, P, R). From V and R: I = V / R (Ohm's law, DC and AC). From P and V: I = P / V (DC) or I = P / (V × PF) (1-φ AC) or I = P / (√3 × V × PF) (3-φ AC). Solve for the unknown directly using the embedded calculator above.
Use NEC 430.250 for motor full-load current — never compute from HP. NEC requires that motor branch-circuit conductors and protection be sized from Table 430.250 FLA values, NOT from nameplate or computed HP/V. A 50 HP 460 V 3-phase motor is 65 A per Table 430.250 — even if the nameplate shows 62 A. The Code values include service-factor margin.
Apply the 125 % continuous-load multiplier. NEC 210.19 / 215.2 / 430.22: continuous loads (≥ 3 hours) and motor loads are sized at 125 % of nameplate. A 65 A motor branch needs conductors rated ≥ 65 × 1.25 = 81.25 A → #4 AWG copper THWN-2 (85 A). Failing this is the most common branch-circuit code violation in industrial design.
Cross-check current against the NEC 310.16 ampacity column. Wire ampacity must be ≥ derated current. NEC 310.16 gives ampacity by AWG and insulation temperature (60 / 75 / 90 °C). Most modern THHN/THWN-2 is sized to the 75 °C column unless terminations are 60 °C-rated (small breakers, devices). See /wire-size/ for the full sizing engine.

Worked example — 25 HP 460 V motor branch

Specify the branch circuit for a 25 HP 460 V 3-phase NEMA Premium induction motor, NEMA Code Letter G:

Step 1 — full-load current: NEC Table 430.250 → 25 HP @ 460 V 3-φ = 34 A FLC. Use this, not nameplate.

Step 2 — branch conductor sizing: 34 × 1.25 = 42.5 A minimum ampacity per NEC 430.22. Look up NEC 310.16 75 °C Cu: #8 AWG = 50 A. Use #8 AWG copper THWN-2.

Step 3 — short-circuit / ground-fault protection: NEC 430.52 + Table 430.52: inverse-time breaker = 250 % FLC = 85 A → next standard NEC 240.6 size = 90 A breaker. (For dual-element fuse: 175 % × 34 = 60 A fuse.)

Step 4 — overload protection: NEC 430.32 → 115 % FLC = 39 A overload heater (or 125 % for 1.15 SF motor = 42.5 A). Set the contactor / starter to trip at 39 A continuous.

Step 5 — locked-rotor current: K_NEMA = 5.6 (Code G). I_start = 5.6 × 25 × 1 000 / (1.732 × 460) = 176 A (5.2 × FLC). Verify the upstream feeder voltage drop during start-up is ≤ 15 % per NEMA MG 1 — at 460 V × 0.15 = 69 V allowable drop during start.

AC vs DC current — when each one applies

Aspect	Direct current (DC)	Alternating current (AC)
Direction	One way (constant polarity)	Reverses 50 / 60 times per second
Ohm\'s law	I = V / R (R real)	I = V / Z (Z complex impedance)
Power formula	P = V × I	P = V × I × cos φ
Voltage drop calculator	V_drop = I × R (resistance only)	V_drop = I × (R cos θ + X sin θ)
Common applications	Battery, solar PV, EV pack, electronics, telecom 48 V	Grid distribution, residential, industrial motors
Conductor sizing	By I and resistance only	By I, X, frequency, and PF
Examples — example of direct current and alternating current	9 V battery powering an LED. EV traction motor (DC after inverter switching).	120 V wall outlet. 3-phase 480 V industrial feeder. 50 Hz UK / 60 Hz US.

Motor current — full-load, starting, locked-rotor

Full-load current (FLC)

Full-load current is the steady-state current a motor draws at nameplate horsepower and rated voltage. NEC 430.250 (three-phase) and 430.248 (single-phase) provide standardised FLC values that supersede the motor nameplate for branch-circuit sizing — see the 3-phase motor current chart above. For odd HP values, interpolate or use the next-larger standard value.

Locked-rotor / starting current

Across-the-line motor starting current (LRA) is typically 5–8 × FLC for NEMA Design B induction motors. Compute it from the NEMA Code Letter on the nameplate (A through V) — each letter encodes locked-rotor kVA per HP. Soft starters reduce the inrush to roughly 2–4 × FLC, and VFDs limit it to ≤ 1.5 × FLC. The figure is needed to size upstream protection and to verify the voltage dip at start-up stays within NEMA MG 1 limits.

Load current — operating vs nameplate

The actual operating current at any moment varies with shaft load, voltage, and time, and is always less than or equal to FLC for a properly-sized motor. Use FLC (the worst case) for branch-circuit sizing; use the measured operating current — via clamp meter or VFD display — for energy analysis and PF correction sizing.

Alternating current — formula, RMS, examples

AC current formula and RMS

The instantaneous alternating current waveform is i(t) = I_peak × sin(2π × f × t + φ). The RMS value used in every power calculation is I_RMS = I_peak / √2. A 120 V RMS outlet has 170 V peak; a 100 A RMS feeder has 141 A peak. RMS is the DC equivalent that delivers the same average power into a resistor — which is why every wire ampacity, breaker rating, and conductor spec is given in RMS.

AC current example

A 1 500 W 120 V AC space heater (resistive, PF = 1) draws I = P / V = 1 500 / 120 = 12.5 A RMS, peaking at 17.7 A instantaneous. The conductor (typically #14 AWG) must handle the 12.5 A continuous load with a 15 A breaker. The single-phase AC current formula is I = P / (V × PF); the three-phase form is I = P / (√3 × V × PF).

Voltage and current relationship in AC

In a purely resistive load, voltage and current are in phase (φ = 0). In a purely inductive load (a motor coil or transformer winding), current lags voltage by 90°. In a purely capacitive load (a capacitor bank), current leads voltage by 90°. Real loads are a mix — characterised by power factor PF = cos φ. This phase relationship between voltage and current governs every AC power calculation.

Phase current — line vs phase, balanced vs unbalanced

In a balanced three-phase Y (wye) system, line current equals phase current — the conductor going into the load and the conductor on each leg of the Y carry the same magnitude. In a balanced three-phase Δ (delta) system, line current = √3 × phase current: phase current flows around the delta loop while line current is the vector sum of two phase currents. For a balanced 480 V Δ load drawing 100 A line current, each Δ branch carries 100 / √3 = 57.7 A. The full Y/Δ converter is at /three-phase-power/.

Frequently asked questions

How to calculate power from voltage and current?: For DC or resistive AC: P (W) = V (volts) × I (amps). For single-phase AC with reactive load: P = V × I × cos φ where cos φ is power factor (typically 0.85–0.95 for motors). For three-phase AC: P = √3 × V_LL × I × cos φ. A 480 V × 50 A 3-φ motor at PF 0.9: P = 1.732 × 480 × 50 × 0.9 = 37 411 W ≈ 37.4 kW.
How to calculate power using voltage and current?: Same as the previous formula — P = V × I × PF for AC, P = V × I for DC. The "current voltage power formula" is the foundation of the V-I-P-R triangle: any one of the four (V, I, P, R) can be derived from any two of the others using Ohm's law (V = I × R) and Joule's law (P = V × I = I² × R = V² / R). For AC, multiply by power factor.
How to find resistance with voltage and current?: R = V / I (Ohm's law, rearranged). A 12 V battery driving 0.5 A through a load: R = 12 / 0.5 = 24 Ω. For AC circuits with reactive components, what you actually compute is impedance Z, not pure resistance: |Z| = V / I (magnitude); to separate R and X you need a phase measurement. For DC and purely resistive AC, R = V / I is exact.
How to calculate resistance with voltage and current?: Identical answer: R = V / I. A 240 V circuit drawing 8 A through a heater coil: R = 240 / 8 = 30 Ω. The heater element dissipates P = V × I = 240 × 8 = 1 920 W, equivalent to P = V² / R = 240² / 30 = 1 920 W or P = I² × R = 64 × 30 = 1 920 W. All three forms agree (Joule's law).
How to calculate power voltage and current?: Use the V-I-P-R triangle. Given any two of (V, I, P, R), compute the other two. The four canonical equations: V = I × R, P = V × I, P = I² × R, P = V² / R. For AC, multiply current-voltage products by power factor (cos φ). The embedded calculator handles every combination — see /power/ for the full V-I-R-P engine.
How to calculate motor starting current?: Motor starting current (= locked-rotor amperage, LRA) is typically 5–8 × full-load current for an across-the-line started induction motor. NEMA Code Letters A through V (on the nameplate) indicate the locked-rotor kVA per HP at rated voltage: Code G ≈ 5.6, Code H ≈ 6.3, Code J ≈ 7.1, Code K ≈ 8.0. For a 50 HP Code G motor: LRA ≈ 50 × 5.6 × 1000 / (1.732 × 460) = 351 A vs FLA of 65 A — a 5.4 × inrush. Use a soft-starter or VFD to limit inrush.
How to calculate the starting current of a motor?: Same calculation as the previous answer — apply the NEMA Code Letter from the motor nameplate. LRA = (Code Letter kVA / HP) × HP × 1000 / (V_LL × √3) for 3-phase. Or use the rule of thumb: starting current = 6 × FLA for typical NEMA Design B motors. For premium high-efficiency motors (Code F or G), starting current can be up to 8 × FLA — verify with the manufacturer data sheet.
How to calculate starting current of motor?: Identical: I_start ≈ NEMA_code_kVA × HP × 1000 / (V_LL × √3). Use the actual nameplate Code Letter — designs vary. NEMA Design B (most industrial motors): Code G or H, ~ 5.5–6.5 × FLA. NEMA Design D (high-slip, hoist motors): Code A or B, ~ 3 × FLA. NEMA Premium / IE3 / IE4: often higher LRA than older Class B motors due to better magnetic steel.
What is full load current?: Full load current (FLC or FLA) is the steady-state current a motor (or load) draws at its rated horsepower output and rated voltage. For 3-phase induction motors, NEC Table 430.250 lists standardized FLC values that supersede the nameplate for branch-circuit sizing — e.g., 50 HP @ 460 V 3-φ = 65 A FLC per NEC. The table values include some margin above typical nameplate values to ensure conductor and breaker headroom.
What is load current?: Load current is the current actually drawn by a connected load at any moment — varies with applied voltage, load condition, and (for motors) shaft load. Not the same as full-load current: a motor lightly loaded may draw 30 A even though its FLA is 65 A. For sizing protection and conductors, always use the full-load current (or NEC nameplate equivalent), not the measured operating load.

The ampere — defined by Ampère's force law (1820)

The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed one metre apart in vacuum, would produce between these conductors a force equal to 2 × 10⁻⁷ newton per metre of length. The unit is named for André-Marie Ampère, the French physicist who in 1820 first quantified the magnetic force between current-carrying wires and laid the mathematical foundation for electromagnetism.

9th Conférence Générale des Poids et Mesures (CGPM) → Resolution 2 (1948) — definition of the ampere

Related calculators and references

Sources and further reading

NFPA. NFPA 70 — National Electrical Code (2023). Articles 220, 240, 310, 430.
NEMA. NEMA MG 1-2021 — Motors and Generators, Part 10 (Code Letters), Part 12 (FLC).
IEEE. IEEE Std 141-1993 (Red Book) — Recommended Practice for Electric Power Distribution.
IEC. IEC 60364 — Low-voltage electrical installations.
Stevenson, W.D. Elements of Power System Analysis, 4th ed., McGraw-Hill, 1982.
Mike Holt Enterprises. Understanding the National Electrical Code, Volume 2 (Articles 500–820). Industry reference for motor branch and feeder sizing.