Ohm's Law Calculator

Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across them. This holds for many materials over a wide range of voltages and currents, provided the resistance of the component stays constant. It applies to circuits containing only resistive elements, with no capacitors or inductors, whether the driving voltage is constant (DC) or time-varying (AC). It is usually written three ways, all rearrangements of each other:

where V is voltage in volts, I is current in amperes, and R is resistance in ohms.

The intuition behind it is worth having. Voltage is the electrical pressure pushing charge along, current is the rate that charge flows, and resistance is how much the conductor obstructs it. Raise the pressure and more flows; raise the obstruction and less does. Everything else on this page follows from that one sentence.

Electrical power

Power is the rate at which electrical energy is transferred by a circuit per unit time, expressed in the SI unit of watts. It is typically produced by generators and supplied to homes and businesses through the grid, though batteries and other sources supply it too.

In resistive circuits, Joule's law can be combined with Ohm's law to give three expressions for the power dissipated:

where P is power in watts. Which one to use is purely a question of which two quantities you already know, and all three give the same answer.

The third form, P = I²R, is the one that shapes how electricity is delivered. Because loss rises with the square of the current, halving the current cuts the wasted power to a quarter. That is the entire reason transmission lines run at hundreds of kilovolts: for the same power delivered, higher voltage means lower current, and lower current means far less energy lost heating the wires.

Ohm's law formula wheel

Below is a formula wheel for the relationships between P, I, V and R. It is essentially what this calculator does, and it is just a representation of the algebra above. To use it, choose the quantity you want to find in the middle of the wheel, then pick the expression in that quadrant that uses the two values you already know.

Twelve expressions look like a lot to remember, and they are not worth memorising. Every one comes from substituting V = IR into P = VI. Knowing those two and being willing to do a line of algebra gets you the other ten.

A worked example

Take a small appliance drawing 0.2 amperes from a 110 volt supply. The resistance is V divided by I, which is 110 / 0.2 = 550 ohms, and the power is V times I, which is 110 × 0.2 = 22 watts. From those two known values everything else about the circuit follows without measuring anything further.

The calculator above works the same way. Fill in exactly two boxes and it solves for the remaining pair, showing which formula it used and substituting your numbers into it.

When Ohm's law does not apply

This is the part most introductions leave out. Ohm's law is not a fundamental law of nature in the way conservation of energy is. It is a description of how certain materials behave, and plenty of components ignore it entirely.

Materials that obey it are called ohmic, and metals at a steady temperature are the usual example. Non-ohmic components have a resistance that changes with the conditions. A diode conducts freely one way and barely at all the other. A filament lamp grows more resistive as it heats, so a cold bulb draws a large inrush current for the first instant it is switched on, which is exactly when filaments tend to fail. A thermistor is built to change resistance with temperature deliberately. For any of these, plotting current against voltage gives a curve rather than a straight line, and a single resistance value does not describe it.

Temperature matters even for ordinary conductors. The resistance of copper rises by roughly 0.4% per degree Celsius, so a motor winding measured warm reads noticeably higher than the same winding measured cold. At the other extreme, certain materials lose their resistance completely below a critical temperature, which Heike Kamerlingh Onnes discovered in mercury at 4.2 kelvin in 1911. Superconductors carry current with no voltage drop at all, which is the one case where the law simply has nothing to say.

Resistance itself is not a fixed property of a substance either. It depends on the shape of the conductor: R = ρL/A, where ρ is the resistivity of the material, L the length and A the cross-sectional area. Copper has a resistivity of about 1.68 × 10⁻⁸ ohm-metres, which is why a thin, long wire drops more voltage than a short, thick one of the same metal. That relationship is what wire gauge tables encode.

In AC circuits with capacitors or inductors, resistance is replaced by impedance, written Z, which accounts for the way those components shift current and voltage out of step with each other. Ohm's law survives in the form V = IZ, but the quantities become complex numbers rather than plain ones.

Where this gets used in practice

Choosing a resistor for an LED is the classic case. An LED dropping 2 volts and wanting 20 milliamperes from a 5 volt supply needs to lose 3 volts across the resistor, so R = 3 / 0.02 = 150 ohms. The resistor dissipates I²R = 0.06 watts, comfortably inside a standard quarter-watt part. That second calculation is the one people skip, and it is why resistors occasionally char.

Battery life estimates work the same way. A device drawing 0.5 amperes from a 2,000 milliamp-hour cell runs for about four hours, ignoring the cell's own internal resistance, which becomes significant at high currents and is why a battery sags under load.

Fault finding leans on it constantly. A measured resistance far above expectations means a poor connection or a corroded joint; far below means a short. Voltage drop along a cable run, calculated as I × R for the cable itself, is what determines whether a long circuit needs thicker conductors.

Safety, briefly

Current is what injures people, not voltage, and Ohm's law is what connects the two. Roughly 1 milliampere through the body is perceptible, about 10 to 16 milliamperes is enough that muscles clamp and the person cannot let go, and around 100 milliamperes through the chest can cause ventricular fibrillation. Residual current devices are set to trip at 30 milliamperes in much of the world, and 5 milliamperes for the GFCI outlets used in American bathrooms and kitchens, precisely because those thresholds sit below the dangerous range.

Body resistance is what turns a voltage into that current, and it varies enormously: hundreds of thousands of ohms through dry skin, but as little as a thousand when wet. The same voltage that is harmless dry can be lethal in a bathroom, which is the practical reason for the entire regime of RCDs, bonding and IP ratings around water.

Some history

Georg Simon Ohm published the relationship in 1827 in Die galvanische Kette, mathematisch bearbeitet, working with wires he drew himself and a thermocouple as a stable voltage source, since batteries of the era drifted too much to measure against. His work was received badly at first, dismissed by parts of the German academic establishment as a web of naked fancies, and he resigned his teaching post over it. Recognition arrived nearly fifteen years later when the Royal Society awarded him the Copley Medal in 1841. The unit of resistance carries his name, and the relationship he described underlies more or less every circuit calculation made since.

For circuits more complicated than a single loop, Ohm's law is applied alongside Kirchhoff's two rules: current into a junction equals current out of it, and voltages around any closed loop sum to zero. Those, plus the series and parallel rules for combining resistances, cover the vast majority of practical DC analysis.