Ohm's Law Calculator

For a resistive component, the current through it is proportional to the voltage across it:

$V = IR \quad\Longrightarrow\quad I = \frac{V}{R}, \quad R = \frac{V}{I}$

Symbols and SI units:

• $V$ — potential difference across the component, volts (V)
• $I$ — current through the component, amperes (A)
• $R$ — resistance, ohms (Ω)

When it applies: to ohmic devices — resistors, most wires, heating elements — at a steady temperature. Diodes, LEDs, transistors and lamps are non-ohmic: their resistance changes with the operating point, so $V = IR$ describes only one instant on their curve, never the whole device.

The assumption people forget: $V$ and $I$ must belong to the same element. Using the supply voltage with the current through one resistor of a divider is the most common way to get a wrong resistance.

Combining Ohm's law with $P = VI$ gives three equivalent power forms:

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

with $P$ in watts (W). Use $I^2R$ when you know the current, $V^2/R$ when you know the voltage.

In a series circuit, one current flows through everything:

$R_{\text{total}} = R_1 + R_2 + \cdots, \qquad I = \frac{V_{\text{supply}}}{R_{\text{total}}}$

and the voltage divides in proportion to resistance, $V_n = IR_n$, summing back to the supply voltage (Kirchhoff's voltage law).

The assumption people forget: this is DC, or steady-state resistive AC. With capacitors or inductors you need impedance $Z$ rather than $R$, and $V = IZ$ with phase angles. Resistance also drifts with temperature — a filament lamp's cold resistance is a fraction of its hot value.

• Leaving current in milliamps — $30$ mA is $0.030$ A. Feeding $30$ into $R = V/I$ gives an answer $1000\times$ too small.
• Mixing kilohms and ohms — $4.7$ kΩ is $4700$ Ω.
• Using the supply voltage for one series resistor — only the voltage across that resistor belongs in $V = IR$.
• Applying Ohm's law to an LED — LEDs need a series current-limiting resistor sized from the difference between supply and forward voltage.
• Ignoring the resistor's power rating — a resistor that must dissipate $0.5$ W will burn out in a $0.25$ W package.
• Forgetting temperature — a hot element has a higher resistance than a cold one.
• Confusing resistance with resistivity — resistivity $\rho$ is a material property measured in ohm-metres, and a conductor's resistance follows from it as $R = \rho L/A$. That is why a longer or thinner wire of the same metal has more resistance than a short fat one.