Ohm's Law Calculator

Background.

In a metal wire or an ordinary resistor held at a steady temperature, current rises in strict step with voltage: double the push and the flow doubles. Georg Simon Ohm set out that proportionality in 1827, and the fixed ratio between the two — the resistance, measured in the unit later named after him — is all that V = I × R says. One ohm is the resistance that lets one ampere through when one volt is applied.

The law earns its place in everyday electronics because most practical questions reduce to it. What resistor keeps a component's current where it should be? How much current will a heating element draw? What is that unmarked resistor, given a voltage and a current you can measure? Each is the same three-way relation solved for a different unknown.

The question people forget to ask is how hot things get. Every ohm in the current's path turns electrical energy into heat at a rate P = V × I watts, and because the substitutions give I²R and V²/R, heat climbs with the square of the current or voltage. Put twice the voltage across the same resistor and it has to shed four times the power. A small through-hole resistor rated at a quarter of a watt will run hot or fail well before the arithmetic looks alarming, so the power figure deserves as much attention as the answer you came for.

The law has limits that matter in practice. It describes components whose resistance stays put. A diode or LED does not behave that way — its current climbs steeply once a threshold voltage is passed — and a lamp filament's resistance rises sharply as it heats. In alternating-current circuits with coils or capacitors, resistance gives way to impedance. For a resistor, a heating element or a stretch of wire, though, three numbers and one multiplication are enough.

What is ohm's law calculator?

Ohm's law states that the current through a conductor is proportional to the voltage across it, provided its temperature and other physical conditions stay the same. The constant of proportionality is expressed as resistance, R = V ÷ I, in ohms, where one ohm equals one volt per ampere. Strictly, the ratio V ÷ I can be worked out for any component at any instant; what makes a device 'ohmic' is that the ratio stays the same as the voltage changes, so a single resistance number describes it at every operating point.

Resistance itself comes from the material and the shape of the conductor: R = ρ × L ÷ A, where ρ is the resistivity, L the length and A the cross-sectional area. Double a wire's length and its resistance doubles; double its cross-section and the resistance halves. Copper, at about 1.68 × 10⁻⁸ Ω·m at 20 °C, works out to 0.0168 Ω for every metre of 1 mm² wire, which is why cable runs only become a problem when they are long or the current is large. Since the 2019 redefinition of the SI, the ohm has rested on fundamental constants: national laboratories realise it through the quantum Hall effect, whose von Klitzing constant h/e² is about 25,812.807 Ω.

How to use this calculator.

1. 01In Solve for, pick the quantity you do not know: voltage, current or resistance. Its own box is ignored, so it can be left blank.
2. 02Enter the other two in base units — volts, amperes and ohms. 20 mA is 0.02 A, 250 µA is 0.00025 A, and 4.7 kΩ is 4,700 Ω.
3. 03If you are measuring rather than designing, put the meter across the component for voltage and in series with it for current. A resistance reading taken on the board can be thrown off by parallel paths through other parts, so for a trustworthy value switch off and lift one leg of the resistor first.
4. 04Use the voltage across the one component you are studying, not the supply voltage, unless that component is the only thing in the circuit. A resistor in series with an LED only sees what the LED leaves over.
5. 05If several resistors are involved, combine them into one equivalent value first; the calculator takes a single resistance.
6. 06Compare the power figure with the part's wattage rating and leave headroom, since heat rises with the square of the current.

The formula.

Whichever quantity you pick in Solve for is found from the matching arrangement of Ohm's law: V = I × R, I = V ÷ R or R = V ÷ I, with V in volts, I in amperes and R in ohms. Power then follows as P = V × I in watts, using the value just solved together with the two you entered. P = I² × R and P = V² ÷ R are the same quantity rewritten, so all three agree. Two requests have no finite answer and return an error instead. Asking for current through 0 Ω describes a perfect short circuit, where the formula predicts unlimited current; in reality the wiring and the source's own internal resistance set the limit. Asking for resistance with 0 A flowing describes an open circuit, whose resistance is effectively unbounded. Values are treated as magnitudes, so the direction of current and polarity are not tracked.

The straight-line relationship has a physical origin. In a metal, the electric field pushes free electrons along, but they keep colliding with the vibrating atomic lattice, so instead of accelerating without limit they settle at an average drift speed proportional to the field. At the scale of the material that is the law in its local form, current density J = σE, with σ the conductivity; scaled up to a whole component of length L and area A it becomes V = I × R with R = L ÷ (σA).

The same picture shows where the model stops working. Heat the lattice and collisions become more frequent, so a metal's resistance rises with temperature, by roughly 0.39 percent per degree Celsius for copper near room temperature. In a semiconductor junction current depends exponentially on voltage, so no single R describes a diode. With alternating current through coils or capacitors, voltage and current fall out of step and the ratio becomes an impedance with a phase angle. The arithmetic here assumes one fixed, real resistance: direct current, or the RMS values of a purely resistive AC load.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Ohm, G. S. (1827). Die galvanische Kette, mathematisch bearbeitet. Berlin: T. H. Riemann. The original monograph in which Ohm states and experimentally validates the linear voltage-current relationship that bears his name.
2. [2]NIST Reference on Constants, Units, and Uncertainty — Ohm (Ω) and the 2019 SI redefinition of electrical units in terms of the elementary charge e, the Planck constant h, the Josephson constant K_J = 2e/h, and the von Klitzing constant R_K = h/e². National Institute of Standards and Technology.
3. [3]IEEE Std 100-2000, The Authoritative Dictionary of IEEE Standards Terms, Seventh Edition. Institute of Electrical and Electronics Engineers. Definitions of voltage, current, resistance, impedance, and the operational form of Ohm's law for DC and AC analysis.
4. [4]Halliday, D., Resnick, R. & Walker, J. (2014). Fundamentals of Physics, 10th ed., Wiley. Chapter 26, sections 26-4 to 26-6, on resistance and Ohm's law, and Chapter 26 problem set on power dissipation and the I²R / V²R forms.
5. [5]Feynman, R. P., Leighton, R. B. & Sands, M. (1964). The Feynman Lectures on Physics, Volume II, Chapter 22 'AC Circuits' and Chapter 32 'Refractive Index of Dense Materials' — Feynman's derivation of why ordinary resistors are ohmic (the Drude model) and why semiconductors are not.
6. [6]Klitzing, K. v., Dorda, G. & Pepper, M. (1980). New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance. Physical Review Letters, 45(6), 494–497. Peer-reviewed paper establishing the quantum Hall resistance standard now used to define the ohm, and discussing where macroscopic Ohm's law fails at the quantum scale.
7. [7]Shockley, W. (1949). The theory of p-n junctions in semiconductors and p-n junction transistors. Bell System Technical Journal, 28(3), 435–489. The original paper deriving the exponential I-V relationship of a semiconductor diode — the canonical example of a non-ohmic device for which Ohm's law fails.