Ohm's Law Calculator — Voltage, Current and Resistance

Ohm's Law is one of the most fundamental relationships in electronics and electromagnetism. It states that the current flowing through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance. First formulated by Georg Ohm in 1827, it underlies the design of every electrical circuit from a torch to a data centre.

The law is expressed as a simple triangle: V = IR. Know any two of the three quantities and you can always find the third. The calculator below does exactly that — it opens with a current of 2 A through a 10 Ω resistor, which gives 20 V across it.

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What Is Ohm's Law? The Water-Pipe Analogy

Before the algebra, it helps to have a physical picture. Electricity in a wire behaves remarkably like water in a pipe, and the analogy holds well enough to carry you through most of an introductory course.

Voltage Is the Pressure

Voltage is the electrical pressure pushing charge around the circuit. A water tank raised high above a pipe creates high pressure; a battery with a large potential difference creates a strong push on the electrons. Nothing flows without it. Voltage is not something a wire "has" on its own — it is always a difference between two points, which is why it is properly called potential difference.

Current Is the Flow Rate

Current is how much charge passes a point each second, exactly as the flow rate of a pipe is how much water passes each second. One ampere is one coulomb of charge per second — about 6.24 × 10¹⁸ electrons streaming past every second. Crucially, current is the same all the way around a simple loop: charge is not consumed by a resistor any more than water is consumed by a narrow section of pipe.

Resistance Is the Narrowness

Resistance is how strongly the conductor opposes that flow — the pipe's narrowness. A thin, long, constricted pipe passes less water for the same pressure. A thin, long, poorly-conducting wire passes less current for the same voltage.

Put those three together and Ohm's Law is almost a statement of common sense: more pressure gives more flow; more resistance gives less flow.

The analogy has limits — water is pushed by gravity while charge is pushed by an electric field, and water leaks while charge does not — but it correctly predicts the direction of every change you can make in a simple circuit.

How Do You Calculate Voltage, Current and Resistance?

$V = IR \quad \Leftrightarrow \quad I = \frac{V}{R} \quad \Leftrightarrow \quad R = \frac{V}{I}$

Symbol	Quantity	SI Unit
V	Voltage (potential difference)	Volt (V)
I	Current	Ampere (A)
R	Resistance	Ohm (Ω)

The Ohm's Law Triangle

A common memory aid places V at the top of a triangle with I and R side by side beneath it. Cover the quantity you want and the remaining two show the operation: cover V and you see I × R; cover I and you see V over R.

It is a useful crutch, but the algebra is worth internalising directly — the triangle stops helping the moment a problem involves power, two resistors, or a changing quantity.

Which Form Do You Need?

• You know a supply voltage and a component's resistance, and want the current it will draw → use $I = V/R$.
• You measured a voltage and a current, and want to characterise the component → use $R = V/I$.
• You know the current a component needs and its resistance, and want the voltage to supply → use $V = IR$.

How Much Power Does a Resistor Dissipate?

A resistor converts electrical energy into heat. The power consumed is:

$P = VI = I^2 R = \frac{V^2}{R}$

Symbol	Quantity	SI Unit
P	Power	Watt (W)

All three forms are algebraically identical — substitute Ohm's Law into $P = VI$ and you get the other two. Which one you reach for depends on what you already know.

Why the I²R Form Explains the National Grid

The $P = I^2R$ form carries a consequence that shapes the entire electricity network: power lost as heat rises with the square of the current. Halving the current cuts the losses to a quarter.

That is precisely why electricity is transmitted at hundreds of thousands of volts rather than at household voltage. To deliver a given power, high voltage means low current, and low current means small $I^2R$ losses in the cables. The worked example below puts real numbers on it.

Worked Examples

Why Doesn't Ohm's Law Work for Every Component?

Ohm's Law is not a law of nature in the way that conservation of energy is. It is a description of how some materials behave, and plenty of components ignore it.

Ohmic Conductors

A component is ohmic if its resistance stays constant regardless of the voltage applied. Plot current against voltage and you get a straight line through the origin. Most metals at constant temperature behave this way — copper wire, nichrome heating elements, and standard resistors.

Non-Ohmic Components

• Filament lamps. As current heats the filament, its resistance climbs steeply. The V–I graph curves over: doubling the voltage produces less than double the current.
• Diodes. Almost no current flows below the forward voltage (~0.7 V for silicon), then current rises very steeply. In reverse, essentially nothing flows at all. Resistance depends on the direction of current — see the p-n junction for why.
• Thermistors. Resistance falls sharply as temperature rises, the opposite of a metal, which makes them useful as temperature sensors.

For non-ohmic components you can still calculate a resistance at any single operating point using $R = V/I$, but that value is only valid at that point. There is no single resistance that describes the component.

How Does Resistance Depend on the Wire Itself?

Resistance is not an arbitrary number — it follows from the material and the geometry:

$R = \frac{\rho L}{A}$

where ρ is the resistivity (a property of the material), $L$ the length, and $A$ the cross-sectional area.

Longer wire means more resistance; thicker wire means less. This is the water pipe again — a long narrow pipe restricts flow, a short fat one does not.

Why Resistance Rises With Temperature in Metals

In a metal, electrons carry current by drifting through a lattice of vibrating atoms. Heat the metal and the atoms vibrate harder, so electrons collide more often and drift less freely — resistance goes up.

Semiconductors do the opposite. Raising the temperature frees more charge carriers, and that effect outweighs the increased scattering, so resistance falls.

How Do You Measure Voltage, Current and Resistance?

Getting the meter connection right is where most practical marks are lost:

• An ammeter measures current, so it must have the same current flowing through it as the component — connect it in series. An ideal ammeter has zero resistance so it does not change the circuit it is measuring.
• A voltmeter measures the potential difference across a component — connect it in parallel, straddling the component. An ideal voltmeter has infinite resistance so it draws no current of its own.
• An ohmmeter must never be connected to a live circuit. It supplies its own small test current and measures the resulting voltage.

Getting these the wrong way round is not just inaccurate: an ammeter placed in parallel across a supply is a near short-circuit.

Once you are comfortable with a single resistor, the natural next step is combining several — see series and parallel circuits for how resistances add in each arrangement.