Ohm's Law and Resistance Calculator

Physics Electricity and Magnetism • Current and Circuits

Written by STEM Calculators Team Published January 14, 2026 Updated February 24, 2026

1. Ohm’s Law and Resistance Calculator

Solve $$V=IR$$ and compute geometric wire resistance $R=\rho\,\dfrac{L}{A}$ using a resistivity library. Outputs also include conductance $$G=1/R$$ (siemens) and conductivity $\sigma=1/\rho$ (S/m), plus power $$P=VI$$ .

Inputs support: pi, e, sqrt(), sin, cos, exp, log. Use * for multiplication.

Mode + Inputs

Mode: Solve for: Voltage $V$ (V): Current $I$ (A): Resistance $R$ (Ω): Resistivity ρ library: Resistivity $\\rho$ (Ω·m): Wire length $L$:

Cross-sectional area $A$:

I–V chart: Plot current span $I_{max}$ (A): Cursor position $f\in[0,1]$:

f=0.45

Play speed:

In “Wire + Ohm” mode, the calculator uses $R=\rho L/A$ as the resistance in $V=IR$.

Ready

Steps

Enter values and click Solve.

Circuit diagram (from your inputs)

Three common setups (solve $I$, solve $V$, solve $R$)

Highlighted panel matches your “Solve for” choice.

The diagram is illustrative: it shows which quantities are treated as “given” vs “solved” in each setup.

I–V chart (pan/zoom)

Drag to pan • wheel to zoom • double-click resets view

Hover: (I, V)=…

Cursor position $f$ only moves the dot on the plot for reading values. It maps to current as $I_{\text{dot}}=-I_{\max}+f\,(2I_{\max})$ (so $f=0$ is far left, $f=1$ is far right).

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1. Ohm's Law And Resistance Calculator — Theory

1) Ohm’s law

Ohm’s law relates voltage $V$, current $I$, and resistance $R$ in many (approximately) linear conductors:

\[ V = IR. \]

Units: $V$ in volts (V), $I$ in amperes (A), $R$ in ohms ($\Omega$).

2) Resistance of a uniform wire

For a uniform wire of length $L$ and cross-sectional area $A$, the resistance depends on the material’s resistivity $\rho$:

\[ R = \rho\,\frac{L}{A}. \]

Resistivity $\rho$ is measured in $\Omega\cdot\mathrm{m}$. Values depend on temperature and purity.

3) Conductance and conductivity

Conductance $G$ is the reciprocal of resistance (measured in siemens, S):

\[ G=\frac{1}{R}. \]

Conductivity $\sigma$ is the reciprocal of resistivity (units S/m):

\[ \sigma=\frac{1}{\rho}. \]

4) Electrical power (heating)

Power delivered to a resistor can be computed in equivalent ways:

\[ P = VI = I^2R = \frac{V^2}{R}. \]

Large currents can produce significant heating even for small resistances.

5) Special case: $\rho=0$ (ideal superconductor)

If $\rho=0$, then $R=\rho L/A = 0$ in this idealized model, so $G\to\infty$. In real circuits, currents are limited by sources, contacts, and protection devices.

Steps

Circuit diagram (from your inputs)

I–V chart (pan/zoom)

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