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Science Calculator

Ohm’s Law Calculator

Voltage. Current. Resistance.

Solve a resistor

Choose two known quantities.

View results

Enter nonnegative magnitudes with up to twenty significant digits. Scientific exponents run from negative thirty through thirty. Known zeros are interpreted as constraints; they are never replaced by a small positive value.

Calculated quantities and report units

Circuit and planning options

Worked examples

Calculated current

I=20.0000 mAI=20.0000\,\mathrm{mA}

A unique finite passive-resistor operating point is determined.

Steady DC magnitudes for one passive resistor. Voltage, current, resistance and power are nonnegative magnitudes. Signed source conventions and active negative-resistance elements are outside this model. Display uses 6 significant figures; arithmetic on the stated input model does not establish measurement certainty.

Voltage, current, resistance and power

Voltage

V=12.0000 VV=12.0000\,\mathrm V

Current

I=20.0000 mAI=20.0000\,\mathrm{mA}

Resistance

R=600.000 ΩR=600.000\,\Omega

Power

P=0.240000 WP=0.240000\,\mathrm W

Step-by-step Ohm’s law working

Normalize both known inputs into SI units, select a valid rearrangement and retain unrounded exact quantities through the calculation. Square-root results retain their exact radicand until final display rounding. The working below uses base SI units; the result cards use your selected unit for each quantity.

  1. 1. State the passive-resistor model

    Use nonnegative steady DC voltage and current magnitudes for the same passive resistor.

    V=IR,P=VI=I2RV=IR,\qquad P=VI=I^2R

  2. 2. Normalize voltage

    Apply the selected metric prefix exactly before solving. Complete exports retain the source decimal and exact arithmetic certificates.

    V=12.0000 VV=12.0000\,\mathrm V

  3. 3. Normalize resistance

    Apply the selected metric prefix exactly before solving. Complete exports retain the source decimal and exact arithmetic certificates.

    R=600.000 ΩR=600.000\,\Omega

  4. 4. Solve current

    Use the normalized quantities without rounding intermediate results. The positive magnitude is selected for a passive resistor.

    I=VR=0.0200000 AI=\frac VR=0.0200000\,\mathrm A

  5. 5. Solve power

    Use the normalized quantities without rounding intermediate results. The positive magnitude is selected for a passive resistor.

    P=V2R=0.240000 WP=\frac{V^2}R=0.240000\,\mathrm W
What Can You Create?

Build a complete passive-resistor operating record

Solve four quantities from two known values

Select any independent pair among voltage, current, resistance and power. The result retains the two supplied magnitudes and calculates every uniquely determined quantity. Explicit zero-case statuses identify an unenergized resistor, an ideal short, an open-circuit limit or an insufficient set of constraints.

Compare adopted ratings and duration estimates

Inspect dissipated power against a rated power and an editable planning limit. Add a duration to estimate energy in three useful units, with transported charge limited to steady unidirectional DC. These optional calculations remain attached to the chosen operating point and its model assumptions.

Preserve exact input-model arithmetic

Unit scaling and rational operations retain the entered decimals. Square roots remain represented by their exact radicands until display rounding. Complete copies and CSV preserve active inputs, optional estimates and working beyond the visible panel, making a numerical result easier to reproduce and compare.

Ohm’s law formulas and step-by-step resistor examples

For an ohmic passive resistor, V=IRV=IR relates the voltage across the element to the current through it and its resistance. Dissipated power is P=VI=I2RP=VI=I^2R. The rearrangement P=V2/RP=V^2/R requires R>0R>0. The calculator uses nonnegative magnitudes and treats the two known quantities as constraints on the same operating point.

Known voltage and resistance

Divide voltage by resistance to recover current, then calculate power without rounding that current first. A zero resistance is a separate constraint case; it must not be inserted into these denominators as though a finite quotient always existed.

I=VR,P=V2R,R>0I=\frac VR,\qquad P=\frac{V^2}R,\qquad R>0

Known current and resistance

These multiplication forms allow zero magnitudes without division. A specified zero resistance is an ideal short model, while zero current through a specified positive finite resistance is an unenergized point. Neither label describes every physical property of a real connection.

V=IR,P=I2RV=IR,\qquad P=I^2R

Known voltage and current

Resistance is identified when current is positive. If current is zero, inspect voltage before interpreting the result: a nonzero voltage gives an ideal open-circuit limit, whereas two known zeros leave resistance undetermined. Power is still zero for those stated ideal constraints.

R=VI,P=VI,I>0R=\frac VI,\qquad P=VI,\qquad I>0

Known voltage and power

Positive voltage and power determine a finite current and resistance. A positive voltage with zero power instead implies zero current and the ideal open-circuit limit. Positive power at zero voltage has no finite-current solution in this passive-resistor model.

I=PV,R=V2PI=\frac PV,\qquad R=\frac{V^2}P

Known current and power

Positive current makes both divisions defined. A zero supplied power then identifies zero voltage and zero ideal resistance. Zero current and positive power are inconsistent for a finite voltage, while a zero pair does not determine resistance.

V=PI,R=PI2,I>0V=\frac PI,\qquad R=\frac P{I^2},\qquad I>0

Known resistance and power

The positive roots describe magnitudes rather than an inferred voltage polarity or current direction. Irrational roots are retained internally through an exact radicand, so subsequent charge or sinusoidal-peak calculations do not start from an already rounded display value.

I=P/R,V=PR,R>0I=\sqrt{P/R},\qquad V=\sqrt{PR},\qquad R>0

Follow the nominal DC example

Start with V=12 VV=12\,\mathrm V across a resistor with R=600 ΩR=600\,\Omega. Both values are already in base SI units. Divide to obtain current, then use the voltage and unrounded current to obtain dissipated power. Reporting current in milliamps changes the numerical representation rather than the operating point.

I=12 V600 Ω=0.02 A=20 mAI=\frac{12\,\mathrm V}{600\,\Omega}=0.02\,\mathrm A=20\,\mathrm{mA}P=(12 V)(0.02 A)=0.24 WP=(12\,\mathrm V)(0.02\,\mathrm A)=0.24\,\mathrm W

For an adopted rating of 0.5 W0.5\,\mathrm W, modeled utilization is u=(0.24/0.5)×100%=48%u=(0.24/0.5)\times100\%=48\%. At an illustrative planning limit of 50%50\%, allowed dissipation is 0.25 W0.25\,\mathrm W and headroom is 0.01 W0.01\,\mathrm W. That numerical comparison does not establish manufacturer derating or operating temperature.

Check roots and metric prefixes explicitly

R=3 Ω,P=2 W⟹V=6 V,I=2/3 AR=3\,\Omega,\quad P=2\,\mathrm W\quad\Longrightarrow\quad V=\sqrt6\,\mathrm V,\quad I=\sqrt{2/3}\,\mathrm A

The square-root example deliberately avoids a perfect square. Its displayed voltage and current can be rounded independently while the underlying radicands still describe the same exact numerical model. Source decimal arithmetic is exact here; a physical resistor value, applied voltage and measured current are not thereby exact measurements.

1 mΩ=10−3 Ω,1 MΩ=106 Ω1\,\mathrm{m\Omega}=10^{-3}\,\Omega,\qquad 1\,\mathrm{M\Omega}=10^6\,\Omega

Keep RMS, peaks and energy distinct

For a purely resistive AC load, Pavg=VrmsIrmsP_{\mathrm{avg}}=V_{\mathrm{rms}}I_{\mathrm{rms}}. If the waveforms are additionally sinusoidal, Vpeak=2VrmsV_{\mathrm{peak}}=\sqrt2V_{\mathrm{rms}}, Ipeak=2IrmsI_{\mathrm{peak}}=\sqrt2I_{\mathrm{rms}} and Ppeak=2PavgP_{\mathrm{peak}}=2P_{\mathrm{avg}}. These peak relationships should not be applied to arbitrary waveforms or substituted into the RMS power formula.

E=Pt,1 Wh=3600 J,1 kWh=3.6×106 JE=Pt,\qquad 1\,\mathrm{Wh}=3600\,\mathrm J,\qquad 1\,\mathrm{kWh}=3.6\times10^6\,\mathrm J

At the nominal 0.24 W0.24\,\mathrm W operating point for one hour, E=864 J=0.24 Wh=0.00024 kWhE=864\,\mathrm J=0.24\,\mathrm{Wh}=0.00024\,\mathrm{kWh}. For steady unidirectional DC, Q=It=72 CQ=It=72\,\mathrm C over that duration. An AC RMS current does not by itself establish net transferred charge, so that quantity is deliberately withheld in RMS mode.

Why Users Love This Tool

Check domains and preserve the numerical operating point

Explicit ideal and degenerate states

  • Negative magnitude inputs are rejected instead of clamped. A zero denominator leads to a classified constraint case, not a fabricated zero resistance, an arbitrary large current or an unlabelled infinity.
  • All six known pairs have their own valid rearrangements. Positive power cannot coexist with zero voltage or zero current at a finite operating point, and insufficient zero pairs retain their unknown quantities.
  • RMS calculations are limited to a purely resistive load. Sinusoidal peaks require an additional explicit assumption, and net charge is not inferred from RMS current alone.

Exact input-model arithmetic and complete records

  • Metric prefix factors and rational operations preserve the input decimals. Perfect-square roots retain rational values; other roots retain exact radicands until final significant-figure rounding.
  • Rating comparisons use exact arithmetic, including the distinction between being below, at or above the adopted planning limit. The comparison does not infer physical tolerances or thermal performance.
  • Share links retain active numerical choices and report units while pruning unused source buffers. Complete copy, LaTeX and CSV actions retain working and optional estimates when a visual panel is hidden.
Perfect For

For circuit learning and transparent resistor estimates

Physics and electronics students

Practice rearranging the same relationships from different known pairs. Follow metric prefixes, recognize why a zero denominator changes the problem and compare exact root certificates with displayed significant figures. Magnitude assumptions keep square-root sign choices explicit.

Educators preparing worked examples

Show a consistent voltage, current, resistance and power record and explain why an ideal short, an unenergized finite resistor and an ideal open limit are different constraints. Optional duration and planning estimates extend the same operating point without hiding new assumptions.

Readers checking nominal operating records

Compare a stated dissipated power with an adopted rating and chosen planning limit, or review energy over a representative duration. Keep source units and complete arithmetic records with the result, while component qualification and broader AC circuit analysis remain separate tasks.

How It Works

How it works in three quick steps.

1

Choose two independent known magnitudes

Select voltage and resistance, current and resistance, voltage and current, voltage and power, current and power, or resistance and power. Enter nonnegative magnitudes for the same passive resistor and select each unit explicitly. Calculated quantity fields remain disabled while their unit selectors control the reported units. A negative signed source convention or active negative resistance is outside this magnitude model.

2

Check the finite solution and circuit assumption

Read all four quantities together with the result status. Some zero pairs identify a unique unenergized point or an ideal short condition; others leave a quantity undetermined or require an ideal open-circuit limit. Choose steady direct current or purely resistive alternating-current RMS values. Sinusoidal peaks require the additional waveform assumption and are kept separate from RMS magnitudes and average power.

3

Inspect working and retain optional planning estimates

Review exact unit normalization and the appropriate rearrangement before using optional rating or duration estimates. Adopt a rated power and planning percentage rather than treating a numerical comparison as component qualification. Constant-operation duration provides energy and, for unidirectional direct current only, charge. Copy complete results or LaTeX, download arithmetic certificates as CSV, share active settings or print the selected report view.

Download & Print

Save the quantities together with their circuit assumptions

Copy the complete report or LaTeX

Copy summary retains every determined quantity, active input, rating result, duration estimate, sinusoidal peak and working step. Copy LaTeX provides the complete core resistor working for a compatible mathematical editor. Plain-text output converts mathematical notation rather than exposing rendering commands.

Download exact arithmetic certificates

CSV retains the selected units with rational numerator and denominator certificates wherever an exact rational result exists. Other root values retain a signed square-root certificate. Optional estimates and source settings appear in the same rectangular report so another reader can reproduce the numerical model without relying on rounded intermediate values.

Print the selected mathematical report

Print / Save PDF removes editing controls, unrelated navigation and guide text. The report retains the circuit model, status, all determined quantities and active optional estimates. The working toggle controls whether derivation steps appear in the printed view, while complete exports retain every generated step.

FAQ

Frequently Asked Questions

Which two inputs can this Ohm’s law calculator use?
Choose any of the six distinct pairs among voltage, current, resistance and dissipated power. For compatible positive inputs, the calculator derives the remaining two quantities under a passive-resistor model. Each quantity has its own unit selector. Calculated fields are disabled so an unused editing value cannot become an unintended third constraint. If a supplied zero changes the algebra, the result explains whether the operating point is unique, undetermined or inconsistent.
Why are zero voltage, current or resistance not all treated the same way?
Their meaning depends on which quantities are independently known. Zero current with a specified finite resistance gives zero voltage and power. Nonzero voltage with zero current instead describes an ideal open-circuit limit, with no finite resistance value. Zero voltage together with zero current does not identify a unique resistance. The calculator preserves such distinctions instead of replacing zero with an arbitrary small number or dividing by zero.
Why does the tool reject negative electrical inputs?
This interface uses nonnegative magnitudes for one passive resistor. Signed voltage and current require a declared reference direction and polarity convention, while negative resistance represents a different element model. Selecting resistance and power alone also cannot identify a physical polarity from the square-root equations. Taking the positive magnitude makes that assumption explicit. A negative input is therefore a validation error, rather than a value that is silently clamped or reinterpreted.
Can I use the RMS option for any alternating-current circuit?
It applies to a purely resistive load using consistent RMS voltage and current. General alternating-current circuits may need impedance, phase angle and power factor, which are outside this model. The optional peak estimates additionally assume sinusoidal voltage and current. For other waveform shapes, RMS values alone do not determine peaks. Average power remains separate from the peak instantaneous power shown under the sinusoidal assumption.
Does being below the selected rating limit prove that a resistor is suitable?
No. The comparison uses your adopted rated power and chosen planning percentage to identify numerical headroom or an exceedance. Actual component suitability can depend on manufacturer derating, ambient temperature, mounting, cooling, operating voltage and pulse conditions. The default percentage is an illustrative editable planning choice. It is not a universal engineering rule, a thermal calculation or a certification that a particular component is appropriate for an application.
Why do milliohms and megohms have separate unit choices?
The metric prefixes represent very different scales, and their letter case matters in mathematical unit symbols. The interface uses the full names to make the choice clear, then renders the correct symbol in each result. Both conversion factors remain exact in the calculation. Changing a calculated quantity’s report unit changes its displayed number and unit together, while changing a known input’s unit changes how its entered magnitude is interpreted.
How are square-root answers rounded and exported?
The resistance-and-power pair can produce irrational voltage and current magnitudes. The calculation retains the exact square-root radicand and rounds the displayed value once to the selected significant figures. Perfect-square cases retain an exact rational value. Complete CSV reports include either that rational certificate or a signed square-root certificate in the stated unit. Extra displayed digits describe the numerical model and do not establish measurement accuracy or a component tolerance.
What do the optional duration and charge estimates assume?
Energy uses the modeled operating power over the selected duration, with exact conversions between seconds, joules, watt-hours and kilowatt-hours. It assumes a constant or representative average operating point. The AC estimate does not integrate an arbitrary waveform phase or partial cycle. Charge is reported only for steady unidirectional DC, because RMS current alone does not determine net transported charge. Incomplete finite operating points withhold these optional estimates.
About This Tool

About this Ohm’s Law Calculator

The Ohm’s Law Calculator builds a four-quantity operating record from two independent known magnitudes. Rather than limiting every problem to current and resistance, it supports the six distinct pairs among voltage, current, resistance and dissipated power. Each quantity has an explicit unit selector, and unused numeric fields remain calculated outputs rather than hidden extra constraints. This makes the selected starting information inspectable before any rearrangement is used.

Its scope is one passive resistor represented by a steady DC magnitude model or by purely resistive AC RMS quantities. The result separates complete finite operating points from unenergized states, ideal short conditions, underdetermined zero pairs, inconsistent finite constraints and ideal open-circuit limits. These labels preserve mathematical meaning without claiming to reproduce every physical property of a real component or connection. Signed source conventions, reactive impedance and active negative-resistance elements require a different model.

Exact arithmetic preserves the entered decimals and metric conversion factors within the stated numerical model. Square-root results retain exact radicands, and display significant figures are applied only at presentation. Optional rating and duration estimates remain attached to that operating point: a selected planning limit is not component qualification, and an AC energy estimate does not identify net transported charge. Complete copies, controlled LaTeX, arithmetic certificates and active-settings links make the result reviewable. The calculator supports physics learning and nominal numerical checks, while measurement uncertainty, manufacturer tolerances, thermal behavior and full circuit design remain outside the information supplied by two magnitudes.

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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