Resistance Calculator — Ohm's Law, Series & Parallel

Solve Ohm's Law for V, I, or R, plus total series and parallel resistance for any number of resistors. Free instant calculator.

July 14, 2026

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Reference Values

Last verified: Jul 11, 2026

Category	Range	What It Means	Status
Ohm's Law ★	V = I × R	The core relationship between voltage (V, volts), current (I, amps), and resistance (R, ohms). Rearranges to I = V ÷ R or R = V ÷ I to solve for any single unknown given the other two.	★ Best
Solve for Current	I = V ÷ R	Current through a resistor equals voltage across it divided by its resistance.	Good
Solve for Resistance	R = V ÷ I	Resistance equals voltage divided by current — the ratio stays constant for an ohmic (linear) resistor.	Good
Series Resistance (any number of resistors) ★	R_total = R1 + R2 + R3 + ...	Resistors in series share the same current, so their resistances simply add. Total resistance is always larger than the largest individual resistor.	★ Best
Parallel Resistance (any number of resistors) ★	1 ÷ R_total = 1 ÷ R1 + 1 ÷ R2 + 1 ÷ R3 + ...	Resistors in parallel share the same voltage, so their conductances (1/R) add instead of the resistances themselves. Total resistance is always smaller than the smallest individual resistor.	★ Best
Parallel Shortcut (2 resistors only)	R_total = (R1 × R2) ÷ (R1 + R2)	A simplified version of the parallel formula that only works for exactly two resistors — often called the 'product over sum' rule.	Good

Source: Ohm's Law and series/parallel resistance formulas are foundational circuit theory, confirmed against Physics LibreTexts "21.1 Resistors in Series and Parallel" and All About Circuits "Parallel Circuits and Ohm's Law." These are ideal-circuit formulas; real components carry manufacturing tolerances not reflected here.

Worked Examples

Ohm's Law — Solve for Current

Voltage (V): 12 V
Resistance (R): 4 Ω

3 A

I = V ÷ R = 12 ÷ 4 = 3 A.

Ohm's Law — Solve for Resistance

Voltage (V): 9 V
Current (I): 0.5 A

18 Ω

R = V ÷ I = 9 ÷ 0.5 = 18 Ω.

Series Resistance — Three Resistors

R1: 100 Ω
R2: 220 Ω
R3: 330 Ω

650 Ω total

R_total = R1 + R2 + R3 = 100 + 220 + 330 = 650 Ω. Series resistances simply add.

Parallel Resistance — Two Resistors

R1: 100 Ω
R2: 200 Ω

66.67 Ω total

R_total = (R1 × R2) ÷ (R1 + R2) = (100 × 200) ÷ 300 = 20,000 ÷ 300 = 66.67 Ω — less than the smallest resistor (100 Ω).

Parallel Resistance — Three Resistors

R1: 10 Ω
R2: 20 Ω
R3: 30 Ω

5.45 Ω total

1 ÷ R_total = 1/10 + 1/20 + 1/30 = 0.1 + 0.05 + 0.0333 = 0.1833. R_total = 1 ÷ 0.1833 ≈ 5.45 Ω — well below the smallest resistor (10 Ω).

How to Use This Calculator

1

Choose a mode

Ohm's Law solves for voltage, current, or resistance from the other two. Series and Parallel Resistance add up a list of resistors into one equivalent value.
2

For Ohm's Law: pick what to solve for

Select Voltage, Current, or Resistance, then enter the other two known values.
3

For Series or Parallel: enter your resistor values

Add as many resistors as your circuit has using the "+ Add Resistor" button, in ohms. Remove any you don't need with the ✕ button.
4

Read the result

The total (or solved) value updates instantly as you type — no submit button needed.

What Each Value Means

Voltage (V) (volts): Electrical potential difference that pushes current through a circuit, measured in volts. In Ohm's Law, V = I × R.
Current (I) (amps): The rate of electric charge flow through a conductor, measured in amps. In Ohm's Law, I = V ÷ R.
Resistance (R) (ohms (Ω)): A component's opposition to current flow, measured in ohms. In Ohm's Law, R = V ÷ I.
Equivalent (Total) Resistance (ohms (Ω)): The single resistance value that would draw the same total current as an entire series or parallel network, given the same applied voltage.

Frequently Asked Questions

What is Ohm's Law and how do I use it to solve for V, I, or R?

Ohm's Law states V = I × R, where V is voltage in volts, I is current in amps, and R is resistance in ohms. Because it's a simple three-variable equation, knowing any two lets you solve for the third: rearrange to I = V ÷ R to solve for current, or R = V ÷ I to solve for resistance. This calculator's Ohm's Law tab lets you pick which variable to solve for and enter the other two.

How do you calculate total resistance in a series circuit?

Add the individual resistances directly: R_total = R1 + R2 + R3 + ... and so on for as many resistors as the circuit has. This works because resistors in series share the same current path, so their opposition to that current simply stacks. Total series resistance is always greater than the largest individual resistor in the chain.

How do you calculate total resistance in a parallel circuit?

Add the reciprocals of each resistance, then take the reciprocal of that sum: 1 ÷ R_total = 1/R1 + 1/R2 + 1/R3 + ... For exactly two resistors, a shortcut works: R_total = (R1 × R2) ÷ (R1 + R2). Parallel resistors share the same voltage but split the current across multiple paths, which is why the combined resistance is always lower than any single branch.

Why is parallel resistance always less than the smallest individual resistor?

Adding a resistor in parallel opens up an additional path for current to flow, and more paths mean less overall opposition to current — the same reason adding another checkout lane at a store reduces the average wait even if that lane is slower than the others. Mathematically, since 1/R_total is a sum of positive reciprocals, 1/R_total is always larger than any single 1/R term, which means R_total is always smaller than the smallest resistor in the group.

What's the difference between series and parallel resistance, in plain terms?

In series, current has only one path, so every resistor adds directly to the total and current is the same through each one. In parallel, current has multiple paths, so each additional resistor gives current an easier route and total resistance drops. Series total resistance is always bigger than any single resistor in the chain; parallel total resistance is always smaller than any single resistor in the group.