Ohm's Law Calculator — Voltage, Current, Resistance, and Power

The Four Electrical Variables

Ohm's Law Formulas

How to Use the Ohm's Law Calculator

1. Open the Ohm's law calculator.
2. Enter any two of the four values (V, I, R, or P). Leave the other two fields blank.
3. Click Calculate. The tool selects the appropriate formula combination and computes both missing values.
4. The result shows the formula used, the substituted values, and the numerical answer with appropriate units.

Worked Examples

Understanding the Ohm's Law Triangle

The classic Ohm's law triangle is a memory aid for the three primary relationships. Place V at the top of the triangle, I and R at the bottom corners. To find any variable, cover it and read the remaining formula:

• Cover V: multiply I × R → V = IR
• Cover I: V divided by R → I = V/R
• Cover R: V divided by I → R = V/I

The power triangle is analogous with P at the top, V and I at the bottom: P = VI (cover P), V = P/I (cover V), I = P/V (cover I). These triangles are visual shortcuts, but understanding the physics behind each formula produces more reliable calculation than mechanical formula selection.

Series vs. Parallel Circuits

Series circuits

In a series circuit, components are connected end-to-end in a single path. Key properties:

• Current is the same through all components: I_total = I₁ = I₂ = ...
• Voltage divides across components: V_total = V₁ + V₂ + ...
• Resistance adds: R_total = R₁ + R₂ + ...

Apply Ohm's law to the total circuit (using R_total and V_total) to find total current, then apply it again to individual components to find individual voltages.

Parallel circuits

In a parallel circuit, components are connected across the same two nodes. Key properties:

• Voltage is the same across all parallel branches: V_total = V₁ = V₂ = ...
• Current divides: I_total = I₁ + I₂ + ...
• Resistance decreases: 1/R_total = 1/R₁ + 1/R₂ + ... (equivalent resistance is less than any individual resistor)

For two resistors in parallel: R_total = (R₁ × R₂) / (R₁ + R₂). This is often called the "product over sum" formula.

Practical Applications

Selecting resistors for LEDs

LEDs require a current-limiting resistor to prevent burning out. To choose the correct resistor:

1. Find the LED's forward voltage (V_f) from the datasheet — typically 1.8–3.3V depending on colour.
2. Find the LED's recommended forward current (I_f) — typically 10–20 mA.
3. Apply Ohm's law: R = (V_supply − V_f) / I_f
4. Example: 5V supply, red LED (V_f = 2V, I_f = 20 mA): R = (5−2) / 0.02 = 150Ω. Use the nearest standard resistor value (150Ω or 180Ω).

Fuse selection

Fuses protect circuits by breaking the circuit when current exceeds a safe level. To select the correct fuse: calculate normal operating current using I = P/V (for a 230V appliance drawing 500W: I = 500/230 ≈ 2.2A). Choose a fuse rated slightly above normal current (3A fuse) — not 10 times above, which would not protect the circuit.

Cable sizing

Long cable runs add resistance, causing voltage drop. The resistance of a copper cable is R = ρL/A, where ρ is the resistivity (1.68 × 10⁻⁸ Ω·m for copper), L is the length (m), and A is the cross-sectional area (m²). For significant cable runs, calculate the voltage drop V = I × R_cable and ensure it stays within acceptable limits (typically <3% of supply voltage for UK/IET regulations).

Battery life estimation

If you know a battery's capacity in mAh and the circuit's current draw in mA, battery life = capacity / current. But current draw often requires Ohm's law first: if you know voltage (battery voltage) and resistance (circuit load), then I = V/R. Battery life = capacity / I.

Limitations of Ohm's Law

Ohm's law applies to linear (ohmic) components — resistors at constant temperature. Many real-world components are non-linear and do not follow V = IR with constant R:

• Diodes: Current-voltage relationship is exponential (Shockley diode equation), not linear.
• LEDs: A special case of diode. Resistance changes dramatically with applied voltage.
• Incandescent light bulbs: Resistance increases significantly with temperature (tungsten filament at operating temperature is ~10× higher resistance than at room temperature).
• Capacitors and inductors: Impedance depends on frequency (AC circuits); simple DC Ohm's law does not apply.
• Semiconductors: Transistors, FETs, and integrated circuits have complex voltage-current relationships that Ohm's law does not capture.

For DC circuits with resistors, Ohm's law is exact. For AC circuits, use impedance (Z) instead of resistance (R), and the relationship becomes V = IZ where Z is a complex number. The calculator handles DC resistive circuits only.

Safety Note for Practical Applications

Always verify calculations before working on live circuits. Mains voltage (230V in Europe, 120V in North America) is lethal — even seemingly small currents above 100 mA through the body can be fatal. For any mains-connected work, consult a qualified electrician. The Ohm's law calculator is provided for educational and low-voltage hobby electronics use.

Common Questions

What is the difference between AC and DC for Ohm's law?

For pure resistors, Ohm's law works the same in both AC and DC circuits using peak or RMS values consistently. For AC circuits with capacitors or inductors, resistance must be replaced with impedance (Z), which includes a reactive component. Use the calculator for DC resistive circuits or AC circuits where only resistors are involved.

Why does more resistance mean less current?

From I = V/R: with constant voltage, increasing R decreases I proportionally. Resistance opposes the flow of charge — the more opposition, the fewer electrons can flow per second. Think of voltage as water pressure in a pipe and resistance as the pipe's narrowness: higher pressure (voltage) drives more flow; narrower pipe (resistance) restricts it.

Can resistance be negative?

In passive components (resistors), resistance is always positive. However, some active circuit configurations (like tunnel diodes in their negative-resistance region, or active feedback circuits) can exhibit apparent negative resistance — where increasing voltage decreases current. These are advanced concepts outside the scope of simple Ohm's law; the calculator assumes positive resistance.

What is the relationship between watts and joules?

Power (watts) is the rate of energy (joules) conversion: 1 watt = 1 joule per second. A 100W light bulb converts 100 joules of electrical energy to light and heat every second. To find total energy consumed, multiply power by time: E = P × t. One kilowatt-hour (kWh, as used in electricity bills) = 1,000 W × 3,600 s = 3,600,000 J = 3.6 MJ.