AC Ohm's Law Calculator
Enter any two of voltage, current and impedance, each with a phase angle. The third phasor and the power triangle are calculated.
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Estimate only. Not engineering or safety advice. Check the result against the applicable standard and the equipment data, and have a competent engineer review it before it is relied on. Terms of use.
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About this calculator
This page calculates voltage |V|, voltage angle, current |I| and 7 more results from voltage |V|, voltage angle, current |I|, current angle and 2 more inputs. Change any value or its unit and the result updates. The steps below show the working for the default values, so you can check each line against your own method.
Limits of this calculator
Exactly two of voltage, current and impedance are needed. A blank angle on a value you enter counts as 0°, so a resistor is an impedance with a blank or zero angle. For a purely resistive circuit the DC Ohm's law calculators give the same magnitudes.
Cross-check: 36 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review.
Verification status: Engineering reference
Engineering reference. Formula and method documented and tested against separately coded reference calculations. Not yet Verified: the evidence listed on this page is still needed.
What this calculator checks
- The arithmetic of the published formula for the values you entered, in the units shown.
What remains unverified
- That the inputs suit your application. Take ratings, resistances and constants from the manufacturer data sheet or project specification.
Verification register entry
| Calculation author | Rahul Sharma (author) |
|---|---|
| Technical review | No independent technical review has been carried out |
| Individual professional approval | Not recorded |
| Formula reference | not recorded |
| Standard and edition | Not applicable: Textbook circuit identity (Ohm's law, power, series/parallel, AC circuit theory); no governing standard |
| Standard review state | Not applicable |
| Scope-screening note | not recorded |
| Cross-check test cases | 36 reference vectors (tests/reference_vectors.json) |
| Review date | not recorded |
| Next review date | not recorded |
| Status | Engineering reference |
Needed before this calculator can be marked Verified: reviewer name, qualification and review date; exact formula reference; formula source (textbook or standard); next review date.
Formula
Worked example
| Input | Value |
|---|---|
| Voltage |V| | 230 V |
| Voltage angle (degrees) | 0 |
| Impedance |Z| | 46 Ω |
| Impedance angle (degrees) | 30 |
- I = V / Z = (230 V ∠0°) / (46 Ω ∠30°)
- |I| = |V| / |Z| = 230 / 46 = 5 A
- ∠I = ∠V − ∠Z = 0° − (30°) = -30°
- Z = 39.837 + j23 Ω (resistance 39.837 Ω, reactance 23 Ω)
- S = V × I*: |S| = 230 × 5 = 1,150 VA at ∠30° (∠V − ∠I)
- P = |S| cos θ = 995.93 W Q = |S| sin θ = 575 VAR pf = cos θ = 0.866
Assumptions
- Steady-state sinusoidal AC at one frequency
- Voltage and current are RMS values
- Angles in degrees; a positive impedance angle is inductive and the current lags the voltage
Exactly two of voltage, current and impedance are needed. A blank angle on a value you enter counts as 0°, so a resistor is an impedance with a blank or zero angle. For a purely resistive circuit the DC Ohm's law calculators give the same magnitudes.
Inputs and results
| Input | Unit | Allowed or shown | Note |
|---|---|---|---|
| Voltage |V| | V | greater than 0 V; may be left blank | Enter any two of voltage, current and impedance and leave the third blank. RMS values |
| Voltage angle (degrees) | (number) | -360 or more, up to 360; may be left blank | Blank counts as 0°. Leave blank when voltage is the value being solved |
| Current |I| | A | greater than 0 A; may be left blank | |
| Current angle (degrees) | (number) | -360 or more, up to 360; may be left blank | Blank counts as 0°. A negative angle behind the voltage is a lagging (inductive) current |
| Impedance |Z| | Ω | greater than 0 Ω; may be left blank | |
| Impedance angle (degrees) | (number) | -360 or more, up to 360; may be left blank | Positive for an inductive load, negative for a capacitive load, 0 for a resistor |
| Result | Unit | Allowed or shown | Note |
|---|---|---|---|
| Voltage |V| | V | Shown to 3 decimal places | |
| Voltage angle (degrees) | (number) | Shown to 2 decimal places | |
| Current |I| | A | Shown to 4 decimal places | |
| Current angle (degrees) | (number) | Shown to 2 decimal places | |
| Impedance |Z| | Ω | Shown to 3 decimal places | |
| Impedance angle (degrees) | (number) | Shown to 2 decimal places | |
| Apparent power |S| | VA | Shown to 2 decimal places | |
| Real power P | W | Shown to 2 decimal places | |
| Reactive power Q (+ inductive) | VAR | Shown to 2 decimal places | |
| Power factor | (number) | Shown to 4 decimal places |
How it is calculated
Each input is converted to the base unit of its quantity, the formula above is applied in the order shown in the worked example, and each result is shown in the unit you choose. Results are held at full precision and rounded only for display, except where a step selects a standard size, as the worked example shows. A value outside its allowed range is refused with a message instead of giving a result.
How the result changes with voltage |v|
| Voltage |V| (V) | Voltage |V| (V) | Voltage angle | Current |I| (A) |
|---|---|---|---|
| 23 | 23 | 0 | 0.5 |
| 57.5 | 57.5 | 0 | 1.25 |
| 115 | 115 | 0 | 2.5 |
| 230 | 230 | 0 | 5 |
| 460 | 460 | 0 | 10 |
| 920 | 920 | 0 | 20 |
| 2,300 | 2,300 | 0 | 50 |
Other inputs are the same as in the worked example above.
Standards and further reading
These are textbook relationships (Ohm's law, series and parallel networks, AC phasors, three-phase quantities). No standard sets the method; standards apply when the result feeds a design, for example cable or protection selection.
Frequently asked questions
What do I need to enter?
Enter voltage |V|, voltage angle (degrees), current |I|, current angle (degrees), impedance |Z| and impedance angle (degrees). Change the unit of a value with its selector and the result stays the same.
What does this calculator assume?
Steady-state sinusoidal AC at one frequency. Voltage and current are RMS values. Angles in degrees; a positive impedance angle is inductive and the current lags the voltage.
Which calculators should I use next?
Common next steps are Watts, Volts, Amps, Ohms (any two), Ohm's Law, Series RLC Impedance and Power Factor. The related links at the bottom of this page open them.
How accurate are the results?
Every figure comes from the same tested engine as the Elecmetric calculators and is meant for estimating. 36 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review. Check design values against the standard and the equipment data you work to.
Formula guides and reference
Longer explanations with worked examples and tables, written for the same topic.
- AC Circuit Formulas: Reactance and Impedance: AC circuit formulas: RMS and peak, frequency and period, inductive and capacitive reactance
- Resonance Formulas: Frequency, Q, Bandwidth: Resonance formulas for a series or parallel LC circuit: resonant frequency, reactance at resonance
More Electrical Fundamentals calculatorsAll engineering calculatorsAC Ohm's Law (Phasors) in Elecmetric