Science Calculator

Electrical Power Calculator

Power. Phases. Energy.

Solve electrical power

Declare the circuit and known values.

Circuit model

Calculate

Voltage

Voltage unit

Current

Current unit

View results

Use nonnegative consumed-power magnitudes. AC modes assume sinusoidal steady state; three-phase inputs must be balanced and use line quantities. Enter up to twenty significant digits with scientific exponents from negative thirty through thirty.

Calculated quantity and report unit

Real power

Real power unit

Reporting and energy options

Display significant figures

Show calculation stepsEstimate energy over an interval

Elapsed duration and duty cycle

Total elapsed duration

Duration unit

On-time duty cycle (percent)

The entered power applies during on-time; off-time power is assumed zero. Use full duty if the power input is already a time-averaged consumption estimate.

Estimate adopted energy cost

Worked examples

Calculated real power

P=24.0000\,\mathrm{W}

The selected inputs determine a compatible electrical operating point.

Steady DC electrical input magnitudes. Nonnegative consumed-power magnitudes exclude regeneration. Display uses 6 significant figures; numerical precision does not establish measurement certainty.

Electrical operating record

Voltage

V=12.0000\,\mathrm{V}

Current

I=2.00000\,\mathrm{A}

Real power

P=24.0000\,\mathrm{W}

DC voltage-to-current ratio

V/I=6.00000\,\Omega

This ratio describes the stated DC operating point. It does not establish an ohmic resistance law, a component model or a temperature-independent resistance.

Energy and adopted tariff estimate

Real electrical power is held constant during the on-time fraction of the total elapsed interval. Off-time consumption is assumed zero. This does not model startup, standby consumption, an arbitrary AC partial-cycle phase or mechanical output.

Total elapsed duration

t=3600.00\,\mathrm s

Effective on-time

t_{\mathrm{on}}=3600.00\,\mathrm s

Electrical energy in joules

E=86400.0\,\mathrm J

Electrical energy in watt-hours

E=24.0000\,\mathrm{Wh}

Electrical energy in kilowatt-hours

E=0.0240000\,\mathrm{kWh}

Use $t_{\mathrm{on}}=t(d/100)$ for the supplied duty percentage $d$ , then $E=Pt_{\mathrm{on}}$ .

Step-by-step electrical power working

Normalize known inputs into base SI units and keep exact input-model values through the calculation. Three-phase root factors and reactive magnitudes retain exact radicands until display rounding. The result cards use your chosen report units.

1. Declare the electrical model
Use steady DC magnitudes for electrical input power. This is not a mechanical output or efficiency calculation.
$P=VI$
2. Normalize voltage
Apply the selected SI scale exactly; keep the original input and unrounded model for the inverse calculation.
$V=12.0000\,\mathrm{V}$
3. Normalize current
Apply the selected SI scale exactly; keep the original input and unrounded model for the inverse calculation.
$I=2.00000\,\mathrm{A}$
4. Solve the selected quantity
Retain exact rational quantities and square-root factors until final display rounding. The result cards use the independently selected report units.
$P=VI=24.0000\,\mathrm{W}$

What Can You Create?

Build an electrical input-power and energy record

Solve the unknown electrical quantity

Calculate real electrical power from declared voltage and current magnitudes, or rearrange the same model to recover voltage or current. AC adds a power-factor inverse using independently known real power. Source quantities and report units remain visible so a changed display scale cannot silently change the selected starting constraints.

Separate three AC power quantities

Inspect real, apparent and reactive power together under the sinusoidal model. Balanced three-phase records explicitly use line-to-line RMS voltage, line current and total power. Leading or lagging direction stays an additional supplied choice, while a zero apparent-power ratio is identified as undefined rather than presented as a measured phase relationship.

Estimate energy over a declared interval

Combine a constant on-state power with total elapsed duration and duty percentage. Convert the resulting energy into joules, watt-hours and kilowatt-hours. An optional adopted tariff extends the same record to an energy-only cost without inventing a billing month, live rate, currency conversion or unentered additional charges.

Electrical power formulas and step-by-step examples

Instantaneous electrical power is $p(t)=v(t)i(t)$ . For steady DC magnitudes, $P=VI$ . The AC options below use sinusoidal RMS values and a passive-load factor $f=\cos\varphi$ , with $0\le f\le1$ . The phase displacement is between a corresponding phase voltage and current; it is not inferred by taking a raw line-to-line voltage angle against a line current.

Steady DC input power

The two inverses require a nonzero supplied denominator. If both the supplied power and that multiplier are zero, the selected unknown remains undetermined. This model describes electrical input, with no automatic claim that all of it becomes useful mechanical output.

P=VI,\qquad I=\frac PV,\qquad V=\frac PI

Single-phase sinusoidal RMS power

The RMS product gives apparent power, while the displacement factor selects the average real power. Applying the DC product alone to a non-unity-factor AC load would conflate these two quantities. A power factor is entered as a fraction rather than a percentage.

S=V_{\mathrm{rms}}I_{\mathrm{rms}},\qquad P=Sf

Balanced three-phase line quantities

Voltage is explicitly line-to-line RMS voltage, current is line RMS current and power is the total for all phases. These conventions avoid multiplying total power by another phase count or treating a phase-to-neutral value as a line-to-line voltage.

S=\sqrt3V_{LL}I_L,\qquad P=Sf

Sinusoidal reactive power and sign

A lagging inductive sign is positive under the adopted passive-load convention and a leading capacitive sign is negative. Without that extra direction, only the magnitude is inferred. An input real power above apparent power has no compatible factor in the allowed range.

|Q|=\sqrt{S^2-P^2},\qquad S>0\Rightarrow f=\frac PS

Follow the single-phase example

Use $V_{\mathrm{rms}}=230\,\mathrm V$ , $I_{\mathrm{rms}}=5\,\mathrm A$ and $f=0.8$ . First form the RMS product, then apply the factor. The reactive magnitude follows from the same compatible power triangle, without treating apparent power as energy consumption.

S=(230)(5)\,\mathrm{VA}=1150\,\mathrm{VA}

P=(1150)(0.8)\,\mathrm W=920\,\mathrm W

|Q|=\sqrt{1150^2-920^2}\,\mathrm{var}=690\,\mathrm{var}

A lagging load has $Q=690\,\mathrm{var}$ ; a leading load has $Q=-690\,\mathrm{var}$ . Both directions have the same $f=0.8$ . For an inverse current calculation using the known voltage, real power and factor, $I_{\mathrm{rms}}=920/(230\times0.8)\,\mathrm A=5\,\mathrm A$ .

Retain the three-phase root factor

V_{LL}=400\,\mathrm V,\quad I_L=10\,\mathrm A,\quad f=0.8

P=\sqrt3(400)(10)(0.8)\,\mathrm W=3200\sqrt3\,\mathrm W

The exact numerical model retains the square root until final display rounding. Report units can then present the same total real power in watts or kilowatts. Neither a star nor a delta branch impedance is inferred, and a balanced total-line calculation does not describe unequal phase loads.

Convert duration into energy and an adopted cost

Run the single-phase example over $t=8\,\mathrm h$ with an on-time percentage $d=50$ . The entered load power applies during on-time only. For an adopted energy tariff $\tau=0.15\,\mathrm{USD}/\mathrm{kWh}$ , the following interval estimate assumes zero consumption during the remaining time.

t_{\mathrm{on}}=t\frac d{100}=4\,\mathrm h

E=Pt_{\mathrm{on}}=(0.920\,\mathrm{kW})(4\,\mathrm h)=3.68\,\mathrm{kWh}

C=E\tau=0.552\,\mathrm{USD}

Use full duty when the supplied power already represents the time-averaged draw over the entire interval; applying a second duty reduction would count the same off-time twice. Extra billing charges and varying tariffs are separate from this constant energy-price multiplication. The tool keeps a small cost visible to the selected significant figures rather than claiming a particular invoice rounding policy.

Why Users Love This Tool

Keep circuit assumptions and electrical units inspectable

Compatibility before a numerical answer

Nonnegative magnitude validation rejects malformed strings and negative source values. A zero multiplier receives a domain interpretation instead of an arbitrary floor or a fabricated inverse.
Power-factor solving checks the exact real-to-apparent constraint before generating reactive results. The input circuit convention is retained in every result and active shared configuration.
AC inputs use sinusoidal steady state; three-phase mode also requires balance. The result does not pretend to integrate distorted waveforms, unequal phases or regeneration from nonnegative consumption magnitudes.

Reproducible arithmetic and interval assumptions

Decimal inputs, prefix conversions and duty fractions retain exact rational values. Three-phase and reactive roots preserve exact radicands until the selected display rounding.
An adopted tariff is a user input, not a fetched market rate. Currency codes label that input without changing its numerical magnitude or supplying an exchange conversion.
Complete text and CSV include the active settings and derivation even when the visible steps are hidden. CSV retains rational or signed-square certificates, making independent recalculation possible.

Perfect For

For electricity learning and explicit load estimates

Physics and circuit students

Compare the steady DC product with sinusoidal RMS power and the balanced three-phase line convention. Practice rearranging the same declared relationship, recognize zero-factor domains and interpret the distinct watt, volt-ampere and reactive unit labels.

Teachers building power examples

Use a consistent real-power example to demonstrate apparent power, reactive direction and the power-factor inverse. Continue into a declared duration without losing the circuit assumption, and explain why a factor magnitude cannot determine a leading or lagging sign.

Readers checking energy records

Translate a stated electrical operating point into an interval energy estimate using an explicit on-time percentage. Retain the adopted price, currency label and exact numerical record alongside a cost estimate, while recognizing the additional information needed for an actual utility bill.

How It Works

How it works in three quick steps.

Declare the circuit and selected unknown

Choose steady DC, sinusoidal single-phase AC or balanced sinusoidal three-phase AC. Select real power, voltage or current as the unknown; AC also supports solving power factor. Enter the remaining known magnitudes for one compatible operating point. Three-phase voltage is line-to-line RMS voltage, current is line RMS current and power is total real input power.

Verify units, compatibility and AC power quantities

Read the status before using the answer. Inspect the independently selected input and report units and review the calculation in base SI units. AC results separate real power from apparent and reactive power. Select leading or lagging behavior only when that additional information is known; otherwise the reactive result remains a magnitude. Zero multipliers and inconsistent passive-load factors receive explicit interpretations.

Add an interval and retain the complete record

Optionally enter a total elapsed duration and on-time percentage to estimate electrical energy. An adopted price per kilowatt-hour provides an energy-only cost in the selected currency label. Review the assumed zero off-time consumption and excluded bill charges. Copy the complete report or LaTeX, download exact arithmetic certificates, share validated active settings or print the report with your selected working visibility.

Download & Print

Retain the electrical convention with each saved result

Copy the record or mathematical derivations

Copy summary includes all determined electrical quantities, circuit choices, active duration and tariff estimates, and generated working. Copy LaTeX retains the core electrical derivations for a compatible editor. These actions keep generated working even when its visual section is switched off.

Download a complete arithmetic record

CSV contains source settings, selected units, AC quantities and interval estimates in a rectangular record. Rational values preserve exact numerator and denominator certificates; irrational values retain a signed square certificate. Long integer certificate cells are protected for spreadsheet import instead of being silently rounded to floating-point precision.

Print the selected mathematical report

Print / Save PDF removes editing controls, page navigation and guide sections. The report retains the declared model, compatibility status, determined quantities and enabled interval estimates. Your working toggle controls printed derivations, while the complete copy and CSV exports retain every generated step.

FAQ

Frequently Asked Questions

How do DC, single-phase and three-phase electrical power differ?

DC uses steady voltage and current magnitudes. The single-phase AC model uses sinusoidal RMS voltage and current with an adopted displacement power factor. The balanced three-phase model combines total real power with line-to-line RMS voltage and line RMS current. Its additional square-root factor accounts for the balanced line-quantity relationship. These choices are mathematical circuit assumptions, so changing a model can change the result even when the written input numbers remain the same.

Does three-phase voltage mean line-to-line or line-to-neutral voltage?

This calculator specifically requires line-to-line RMS voltage in the balanced three-phase mode. It does not treat an entered line-to-neutral value as interchangeable or automatically infer a star or delta branch voltage. The current is line RMS current and the real power is the total across all three phases. An unbalanced system or an individual single-phase branch needs additional circuit information and should not be forced into this balanced total-power formula.

Why are watts, volt-amperes and reactive volt-amperes shown separately?

Real power measures average electrical energy transfer and is reported in watts. Apparent power is the RMS voltage-current magnitude under the selected AC convention and is reported in volt-amperes. Reactive power describes the sinusoidal quadrature exchange and uses reactive volt-amperes. They have different interpretations even though their dimensional scales are related. The selected power prefix scales all three consistently, but the result keeps their unit symbols and mathematical roles distinct.

Can power factor determine whether a load is leading or lagging?

A nonnegative power-factor magnitude does not identify the reactive sign by itself. Sinusoidal leading and lagging phase relationships can have the same cosine and therefore the same real power. Choose a direction only when it is supplied by the problem or a suitable measurement. The unknown-direction option reports the reactive magnitude. If apparent power is zero, the real-to-apparent power ratio and physical phase angle remain undefined rather than being inferred from an adopted factor.

What happens when power factor, voltage or current is zero?

A forward calculation with known finite voltage, current and a zero AC power factor can have zero real power but nonzero apparent and reactive power. An inverse calculation is different: zero real power divided by a zero multiplier does not determine a unique unknown. Positive real power with that same zero multiplier is incompatible with a finite operating point. The calculator reports these cases explicitly and withholds optional estimates when the complete point is undetermined.

Can I use these AC results for distorted or unbalanced waveforms?

The AC interface declares sinusoidal steady state, and its three-phase option additionally declares balance. Under those assumptions, the power-factor and reactive-power relationships are appropriate to the stated magnitude model. Harmonic distortion, unequal phases and arbitrary waveform integration require more information than this page accepts. The tool does not use a sinusoidal power triangle as a general distortion calculation or infer an instantaneous waveform from RMS magnitudes alone.

How are operating time, duty cycle and electricity cost calculated?

Enter a total elapsed interval and the percentage during which the stated electrical power applies. Effective on-time is that interval multiplied by the duty fraction, assuming zero off-time consumption. Real electrical power gives energy, and your adopted tariff multiplies kilowatt-hours to estimate an energy-only cost. Currency selection changes the label without exchange conversion. Standby draw, startup, fixed charges, taxes, demand pricing and time-of-use variation require separate inputs or a different billing model.

Does this calculator predict motor output, efficiency or measurement accuracy?

It reports electrical input quantities for the declared operating point. Mechanical shaft output, conversion efficiency, manufacturer tolerances and measurement uncertainty are not supplied by the accepted inputs. Exact rational operations and retained square-root radicands avoid premature numerical rounding, while display significant figures control presentation. That arithmetic precision does not establish physical accuracy. Complete CSV records preserve the adopted inputs and exact numerical certificates so the calculation can be reviewed independently of rounded screen values.

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About This Tool

About this Electrical Power Calculator

The Electrical Power Calculator connects a declared circuit convention with a reproducible numerical operating record. Its starting point is electrical input power, rather than an assumed useful output or an inferred motor efficiency. Steady DC accepts voltage and current magnitudes. Sinusoidal single-phase AC adds a displacement factor, while balanced three-phase AC explicitly uses total power, line-to-line RMS voltage and line RMS current. Selecting the unknown changes which source quantities constrain the calculation, and independently chosen report units preserve the distinction between a source magnitude and its displayed representation.

AC records separate real power, apparent power and reactive power. Those quantities are related under the stated sinusoidal assumptions, but their roles are not interchangeable. A supplied factor magnitude cannot reveal the reactive sign, and zero apparent power cannot establish a measured power ratio. The interface therefore keeps leading or lagging direction explicit and reports incompatible or insufficient constraints before offering optional estimates. It does not infer a circuit topology, harmonic spectrum, unequal phase distribution or regenerative direction from the accepted nonnegative magnitudes.

Duration estimates extend a compatible point over a specified total interval and an adopted on-time fraction. They retain the assumption of zero off-time draw and distinguish electrical energy from instantaneous or average power. A user-adopted tariff supports an energy-only cost estimate with a currency label, without inventing exchange rates or unentered bill charges. Exact rational operations and retained root certificates make the supplied numerical model reproducible; selected significant figures are a presentation choice. Measurement uncertainty, real component behavior, mechanical efficiency and detailed utility pricing remain questions requiring information beyond this mathematical record.

Editorial Transparency

Who maintains this page

Ownership and review

Written and maintained by the Toolarithm editorial team. No review date is shown without a maintained editorial record. No independent professional review is claimed.

Methodology

The method identifies the governing relationship, units, significant assumptions, and educational scope. SI terminology is checked against the BIPM reference.

Read the editorial methodology

Dates and sources

Review dates change only after a substantive method or content check.

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