Ohm's Law Calculator

Background.

This ohm's law calculator solves the foundational equation of direct-current circuit analysis — V = I × R — for whichever of the three quantities you do not know, and then returns the power dissipated by the component for free. Pick a 'solve for' mode, type in the two values you do know, and the tool returns voltage, current, resistance, and power in SI units (volts, amperes, ohms, watts).

The reason this single equation matters so much, and the reason an electrical engineer reaches for it before any more sophisticated tool, is that almost every elementary DC question — what resistor do I need in series with an LED, how much current is my motor drawing, will this wire overheat at 15 A, what is the equivalent resistance of two parallel speakers, how much power does my Raspberry Pi pull at 5 V — collapses to V = IR plus one of its three power siblings: P = VI, P = I²R, and P = V²/R. Those four relationships, sometimes drawn together as 'Ohm's law wheel' or 'power wheel', are the entire algebra of resistive DC circuits.

Georg Simon Ohm published the linear relationship between current and voltage across a conductor in his 1827 monograph 'Die galvanische Kette, mathematisch bearbeitet' ('The galvanic circuit investigated mathematically'), and despite being met with hostility by Berlin's physics establishment for years, the result eventually became one of the most experimentally validated statements in physics. The ohm itself is now a defined SI unit — one ohm is the resistance that produces one ampere of current under one volt of applied potential — and since the 2019 SI redefinition, all three quantities are tied to invariant constants of nature (the elementary charge e for amperes, the Josephson constant K_J = 2e/h and von Klitzing constant R_K = h/e² for the volt and ohm respectively).

Below the widget you will find the derivations of the three power forms, worked examples for the LED-and-series-resistor problem that every electronics hobbyist meets in their first hour, household-circuit math for breaker sizing and extension-cord ratings, the impedance generalization that Ohm's law morphs into for AC analysis, and an honest discussion of where the law breaks down — non-ohmic devices such as semiconductors, incandescent filaments at hot operating temperatures, gas discharges, and any component whose I-V curve is meaningfully nonlinear.

The calculator itself is a thin shell over a pure-function solver registered at ohmsLaw.solve; the same code path is exercised by 19 unit tests covering boundary cases (zero current, zero resistance, very small currents in the microampere range, very large currents in the kiloampere range) so the answer you read here is the same answer used elsewhere in the Quanta engineering toolset.

What is ohm's law calculator?

Ohm's law states that, for an ohmic (linear, time-invariant, passive) conductor at constant temperature, the current I flowing through it is directly proportional to the voltage V applied across it, with the proportionality constant being the conductance G = 1/R, where R is the resistance. The three algebraic forms — V = IR, I = V/R, R = V/I — are mathematically identical; which one you solve depends on which quantity is the unknown in your problem. The law is empirical: it summarizes a vast body of experimental observation rather than being derived from more fundamental principles, although in modern condensed-matter physics it can be understood as a consequence of the Drude model of electrons drifting in a lattice with a characteristic scattering time. Three things follow immediately. First, doubling the voltage across a fixed resistor doubles the current. Second, doubling the resistance at a fixed voltage halves the current. Third, the power dissipated as heat in the resistor — the Joule heating — is P = VI, which by substitution becomes P = I²R or P = V²/R depending on which quantity is held fixed in your design. Ohm's law as stated above applies most cleanly to DC steady-state circuits. In AC circuits the same proportionality survives, but R is replaced by the complex impedance Z, which packages resistance together with the frequency-dependent contributions of inductors and capacitors; voltage and current then become phasors and the law becomes V = IZ. For non-ohmic devices — diodes, transistors, neon bulbs, electrolytes, incandescent filaments hot enough to change resistance with temperature — the linear relationship fails and you need the device's full I-V curve, not a single resistance number.

How to use this calculator.

1. 01Choose which quantity you want the calculator to compute from the 'Solve for' menu — voltage, current, or resistance.
2. 02Enter the two known quantities. Use SI units: volts (V), amperes (A), and ohms (Ω). Convert milliamps to amps by dividing by 1000 (20 mA = 0.02 A) and kilohms to ohms by multiplying by 1000 (4.7 kΩ = 4700 Ω).
3. 03Leave the field for the unknown quantity blank — the calculator ignores it and computes the missing value from the other two.
4. 04Read the primary result (your solved-for quantity) and the power output P, which is always returned in watts regardless of which mode you picked.
5. 05For an LED-and-resistor sizing problem, enter the supply voltage minus the LED forward voltage as 'Voltage', the target LED current as 'Current' (typically 0.02 A for a standard 5 mm LED), and solve for resistance.
6. 06For a 'will this wire overheat?' question, enter the expected current and the wire's resistance per metre times its length, and check the power output against the wire's rated dissipation.

The formula.

The core relationship and its three power forms are:

V = I × R (Ohm's law) P = V × I (electrical power, from the definition of voltage as energy per charge) P = I² × R (substitute V = IR into P = VI) P = V² / R (substitute I = V/R into P = VI)

These four equations form what electrical engineering textbooks call the 'Ohm's law wheel' or 'power wheel': given any two of {V, I, R, P}, you can solve for the other two. The calculator implements the V/I/R triangle directly and returns P alongside as a derived value. Three small but important conventions are baked in. First, all quantities are taken as positive scalars — the calculator does not model signed current direction or polarity, which is the right choice for a steady-state DC magnitude problem. Second, the calculator refuses to divide by zero: if you ask for resistance with current = 0 (an open circuit) or for current with resistance = 0 (a short circuit at finite voltage), it raises an InvalidInputError rather than silently returning Infinity. Third, the law applies to a single ohmic component or to a Thevenin-equivalent of a network. For series circuits, add the individual resistances and apply V = IR to the total. For parallel circuits, add the reciprocals: 1/R_total = 1/R_1 + 1/R_2 + ... and then apply V = IR to the equivalent. The calculator does not perform network reduction for you — feed it the equivalent resistance you have already computed.

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.