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engineering · electrical · circuit-fundamentals

Ohms Law Calculator

Solves Ohm's law and the AC power triangle from any two known values among voltage, current, resistance and power. Use it for quick electrical calculations across single and three-phase circuits.

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Calculator overview

Inputs and outputs

This summary comes from the calculator's published input and output contract.

Inputs

Voltage
About this input

The first of the two known quantities, in the unit implied by the chosen pair, for example volts when the pair starts with voltage.

Unit V Default 240 Range At least 0
Known Pair
About this input

Which two of voltage, current, resistance and power you are entering. The tool solves for the remaining quantities from this pair.

Default Voltage and current Allowed Voltage and current, Voltage and resistance, Current and resistance, Power and voltage, Power and current
Phase
About this input

Single-phase or three-phase, which sets how real, reactive and apparent power relate to voltage and current.

Default Single phase or DC Allowed Single phase or DC, Three phase
Power Factor
About this input

The power factor of the load, between 0 and 1, the cosine of the angle between voltage and current. For DC circuits and resistive AC loads enter 1: DC has no phase angle, so any lower value would wrongly scale the power figures.

Unit fraction Default 1 Range 0 to 1
Current
About this input

The second of the two known quantities, in the unit implied by the chosen pair, for example amperes when the pair includes current. In three-phase mode the resistance this tool expects is the line voltage-to-current ratio rather than a measured per-phase or per-winding resistance, because it does not model the wye or delta connection: entering a per-phase value with the Voltage and resistance pair makes the derived current and power about 1.732 times too high, and with the Current and resistance pair it makes the derived voltage and power about 1.732 times too low.

Unit A Default 12 Range At least 0

Outputs

Apparent Power
About this output

The apparent power, in volt-amperes: voltage times current before the power factor is applied.

Unit VA
Check Power From I Squared
About this output

A cross-check of real power computed as current squared times resistance, in watts. It should match the real power output.

Unit W
Check Power From V Squared Over
About this output

A cross-check of real power computed as voltage squared divided by resistance, in watts. It should match the real power output.

Unit W
Current
About this output

The current through the load, in amperes, whether entered or solved for.

Unit A
Model Status
About this output

The overall check on your entries, shown above the results. It reads OK when the inputs are usable, NOT VALID with a reason when an entry makes the model meaningless, or CHECK with a reason when a result is valid but worth a second look. Read it before you trust the numbers below.

No unit declared
Phase Angle
About this output

The angle between voltage and current, in degrees, whose cosine is the power factor.

Unit degrees
Reactive Power
About this output

The reactive power, in volt-amperes reactive, that oscillates without net work.

Unit var
Real Power
About this output

The real power dissipated, in watts, the part that does actual work.

Unit W
Resistance
About this output

The ratio of voltage to current, in ohms. For DC and for single-phase AC at unity power factor this is the resistance of the load. For three-phase AC, and for any AC load with a power factor below 1, it is the magnitude of the line voltage-to-current ratio -- an impedance-style figure, not a physical resistance -- because this tool does not model the connection (wye or delta) or the reactive part separately.

Unit ohm
Voltage
About this output

The voltage across the load, in volts, whether entered or solved for.

Unit V

What it is

The Ohm's Law Calculator solves a circuit from any two of voltage, current, resistance and power. You choose which pair you know, enter them, and it returns the rest, together with the AC power triangle (real, reactive and apparent power, and the phase angle) for single-phase, DC or three-phase circuits.

Voltage is in volts, current in amperes, resistance in ohms and power in watts or volt-amperes.

Use it for quick circuit arithmetic and as a check on a figure you already have. It solves an idealised circuit: a fixed resistance at a steady operating point, with nothing about how a real load behaves.

Methodology

Purpose and model boundary

This model solves voltage, current, the voltage-to-current ratio, and power from one of five supported pairs of known quantities. It also applies a phase multiplier and scalar power factor to report real, apparent, and reactive power.

It represents one balanced operating point. It is not a network solver, a conductor-sizing tool, or a complex-impedance model.

Inputs and units

  • Known pair selects voltage/current, voltage/resistance, current/resistance, power/voltage, or power/current.
  • First value and second value are positive numbers whose labels and units change with the selected pair.
  • Phase selects single phase or DC, or three phase. The three-phase branch uses a square-root-of-three multiplier.
  • Power factor is a fraction greater than zero and no greater than one. Use one for DC and purely resistive AC.

The workbook computes the two dynamic input labels from the known-pair selection. Inputs must be interpreted with those displayed labels rather than as permanently assigned voltage or current fields.

Governing relationships

Let m = 1 for single phase or DC and m = sqrt(3) for three phase. The selected known pair is rearranged to obtain voltage V and current I:

Known pair Solved voltage Solved current
Voltage and current entered voltage entered current
Voltage and resistance entered voltage V / R
Current and resistance I x R entered current
Power and voltage entered voltage P / (m x V x PF)
Power and current P / (m x I x PF) entered current

The workbook then calculates:

R_ratio = V / I

Real power = m x V x I x PF

Apparent power = m x V x I

Reactive power = Apparent power x sqrt(max(0, 1 - PF^2))

Phase angle = arccos(PF) in degrees, only for 0 < PF <= 1

The two consistency checks are:

Power check 1 = m x I^2 x R_ratio x PF

Power check 2 = m x V^2 / R_ratio x PF

Because R_ratio is defined as V / I, both checks should reproduce the primary real-power result for a valid state.

Calculation sequence

  1. Translate the known-pair and phase dropdowns to workbook branch codes.
  2. Use the selected rearrangement to obtain voltage and current.
  3. Divide voltage by current to obtain the reported ratio.
  4. Apply phase multiplier and power factor to calculate real, apparent, and reactive power.
  5. Calculate phase angle and both alternate real-power checks.
  6. Evaluate the status rules before the displayed results are interpreted.

Outputs and interpretation

Voltage, current, real power, and resistance are primary results. The resistance output is exactly the voltage-to-current ratio. For DC and single-phase unity-power-factor loads this can represent physical resistance. For three-phase operation or power factor below one, it is an impedance-style line-voltage/current magnitude, not a resolved physical resistance, because connection and reactance are not modeled.

Apparent power describes the volt-ampere burden, reactive power the quadrature component implied by power factor, and phase angle the arccosine of power factor. The two power checks demonstrate internal algebraic consistency; they are not independent measurements.

Validation and status logic

The workbook evaluates status in this order; the first matching row is returned.

Condition Returned status
Either known value is zero or negative NOT VALID: both known values must be greater than zero
Power factor is zero or negative, or greater than one NOT VALID: power factor must be between 0 and 1
The selected pair produces a non-positive voltage-to-current ratio NOT VALID: the inputs give a non-positive resistance
None of the preceding conditions applies OK

Assumptions and limitations

The model assumes a balanced sinusoidal three-phase system when that branch is selected and treats voltage as the line value used by its power equation. Power factor is a single user-supplied scalar. Frequency, wye/delta connection, phase impedance, inductance, capacitance, harmonics, non-sinusoidal current, and time-varying behavior are not represented.

The voltage-to-current ratio is fixed at the entered operating point. Real devices can change resistance or impedance with temperature, speed, saturation, frequency, or control state. The model does not reduce series/parallel networks, calculate conductor voltage drop, select protection, or establish code compliance.

Restrictions and non-computing states

Both known values and power factor must be positive, and power factor cannot exceed one. Known-pair and phase values must match the delivered dropdowns. When a division would otherwise fail, workbook guards can produce zero intermediates, but the corresponding NOT VALID status means no result should be used.

Errors and warnings

Contract bounds and dropdowns may be enforced by the LogicCommons proxy before SpreadsheetWeb executes. The workbook’s NOT VALID status describes an invalid electrical/arithmetic state; this calculator has no workbook CHECK branch. A proxy, network, or SpreadsheetWeb service error is a transport failure rather than an Ohm’s-law result.

References

The workbook derives its relations rather than reproducing any table or figure. Ohm's law and the power relations are elementary and are computed directly.

Nothing here is a code calculation. Conductor sizing, protective device selection and voltage-drop limits are governed by the electrical code adopted where the work is built and are outside this tool.

Additional source notes migrated from Methodology

The implemented relations are Ohm’s law, the AC power triangle, the scalar power-factor relation, and the balanced three-phase square-root-of-three relation. See the page’s References section for the listed explanatory sources. No electrical-code sizing rule is implemented.

Frequently asked questions

Why does the page show the same power three times?
Because they are three independent routes to it (`V x I`, `I² x R` and `V² / R`), and on a consistent resistive circuit all three must agree. They are shown so you can see the arithmetic checking itself. If they ever disagree, the inputs are not describing one consistent circuit, and that is worth knowing before you use any of the numbers.
What is the difference between real, reactive and apparent power?
Apparent power is what the conductors and the transformer actually carry, in volt-amperes: voltage times current. Real power, in watts, is the part that does work and appears on the bill. Reactive power, in volt-amperes reactive, is the part that circulates back and forth sustaining magnetic fields in motors and transformers without doing work. Apparent power is what you must size equipment for; real power is what you get for it.
What happens if I set the power factor below 1?
Current stops being proportional to useful power. At 240 V and 12 A the conductors carry 2,880 VA whatever the power factor, but at 0.8 only 2,304 W of that does work; the rest is reactive, and the phase angle opens to about 37 degrees. You are paying to move current that accomplishes nothing, which is why utilities penalise poor power factor and why correction capacitors exist.
Why did my answer change by 1.732 when I selected three phase?
Because three-phase apparent power is `sqrt(3) x V x I`, where the voltage is line-to-line and the current is per conductor. Three conductors each carrying the stated current deliver more than a single-phase pair does. Forgetting or double-applying that factor is the most common arithmetic slip in distribution work. Note too that the tool takes the voltage as line-to-line, which is the usual convention but not the only one in use.
Can I use this for an incandescent lamp or a motor?
Only with care, because neither is a fixed resistance. An incandescent filament's resistance rises roughly tenfold from cold to operating temperature, so a cold-resistance measurement will badly mispredict the running current. A motor's effective impedance varies with load and slip, and its starting current bears no relation to its running current. Ohm's law describes a resistor; real loads are described at one operating point at best.
Does this size my wire or breaker?
No. It solves circuit arithmetic and nothing more. Conductor sizing involves ampacity tables, derating for grouping and ambient temperature, termination temperature limits and voltage drop over the run; protective device selection has its own rules. None of that is here, and none of it follows from Ohm's law alone.
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This page is provided by LogicCommons for informational purposes only. Results are analysis outputs computed from the inputs you supply and are not engineering advice, a design, or a substitute for review by a licensed professional under the codes adopted where the work is built. Verify all inputs and results independently.

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