Equivalent Resistance — How to Find Req (Formula & Method)

What is equivalent resistance?

Equivalent resistance (Req) is the single resistor that draws the same current from a source as the original network. Replacing a network with Req simplifies Ohm’s law checks and power estimates.

Series formula

Req = R1 + R2 + … + Rn

Always greater than the largest individual resistor.

Parallel formula

1/Req = 1/R1 + 1/R2 + … + 1/Rn

Always less than the smallest resistor. Two-resistor shortcut:

Req = (R1 × R2) / (R1 + R2)

Equal resistors: Req = R / N.

How to find equivalent resistance (method)

1. Redraw and label every resistor.
2. Mark pure series and pure parallel groups.
3. Replace the innermost group with its Req.
4. Repeat until one resistor remains.
5. Verify: series totals grow; parallel totals shrink.

Worked combination example

R1 = 1 kΩ in series with (R2 = 2.2 kΩ ∥ R3 = 4.7 kΩ):

1. Parallel: 1497 Ω
2. Series: 1000 + 1497 = 2497 Ω ≈ 2.5 kΩ

Tools

• Parallel Resistor Calculator — enter R1…Rn, get Req, steps, and missing-R mode
• Series-Parallel Circuit Calculator — expression solver for nested networks
• Series vs Parallel Circuits — comparison table and definitions
• Current Divider Calculator — currents after you know the parallel group