parallel circuit resistance calculator

How to use this calculator

This tool finds the equivalent resistance of resistors connected in parallel. In a parallel network, each resistor shares the same voltage, and current splits among branches.

• Enter resistor values in ohms (Ω).
• Use commas, spaces, or line breaks between values.
• Click Calculate to get total resistance instantly.
• Optionally enter source voltage to estimate total and branch currents using Ohm’s law.

Parallel resistance formula

The core formula is:

1 / Req = 1 / R1 + 1 / R2 + ... + 1 / Rn

Then invert the sum:

Req = 1 / (1 / R1 + 1 / R2 + ... + 1 / Rn)

Two-resistor shortcut

If there are only two resistors, you can use:

Req = (R1 × R2) / (R1 + R2)

This is algebraically equivalent and often faster to do by hand.

Worked examples

Example 1: 100 Ω and 200 Ω in parallel

1 / Req = 1/100 + 1/200 = 0.01 + 0.005 = 0.015
Req = 1 / 0.015 = 66.67 Ω

Example 2: 10 Ω, 15 Ω, and 30 Ω in parallel

1 / Req = 1/10 + 1/15 + 1/30 = 0.1 + 0.0667 + 0.0333 = 0.2
Req = 1 / 0.2 = 5 Ω

Why parallel resistance is always lower

Adding more parallel branches gives current more paths to flow. More paths means less total opposition, so equivalent resistance goes down. In fact, the total resistance is always less than the smallest branch resistance (for positive resistor values).

Common mistakes to avoid

• Adding resistors directly (that is only valid for series circuits).
• Mixing units (e.g., kΩ and Ω) without converting first.
• Entering negative resistance values in basic passive circuits.
• Forgetting that a 0 Ω branch creates a short and forces equivalent resistance to 0 Ω.

Practical applications

A parallel circuit resistance calculator is useful in electronics design, troubleshooting, and education. Typical use cases include:

• Designing voltage divider loads and sensor networks.
• Estimating current draw from power supplies.
• Checking equivalent resistance in PCB circuits.
• Learning circuit analysis in physics and electrical engineering classes.

FAQ

Can I use just one resistor?

Yes. If only one resistor is entered, the equivalent resistance is that same value.

What if I enter 0 Ω?

A 0 Ω branch represents an ideal short circuit in parallel, so equivalent resistance becomes 0 Ω.

Does this include resistor tolerance?

No. This calculator uses nominal values only. For tolerance analysis, evaluate best-case and worst-case resistor combinations separately.