Parallel Circuit Calculator Formula

Understand the math behind the parallel circuit calculator. Each variable explained with a worked example.

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Formulas Used

Equivalent Resistance

equivalent_resistance = r_eq

Total Current

total_current = v_supply / r_eq

Current through R1

i_r1 = v_supply / r1

Current through R2

i_r2 = v_supply / r2

Variables

VariableDescriptionDefault
v_supplySupply Voltage(V)12
r1Resistor R1(Ω)100
r2Resistor R2(Ω)200
r_eqDerived value= 1 / (1/r1 + 1/r2)calculated

How It Works

Parallel Resistor Calculation

Parallel resistors share the same voltage. The equivalent is always less than the smallest.

Formula

1/R_eq = 1/R1 + 1/R2

Or: R_eq = (R1 x R2) / (R1 + R2)

Branch currents: I_n = V / R_n.

Worked Example

12 V supply with R1 = 100 and R2 = 200 ohms in parallel.

v_supply = 12r1 = 100r2 = 200
  1. 01R_eq = 1 / (1/100 + 1/200) = 66.67 ohms
  2. 02Total current = 12 / 66.67 = 0.18 A
  3. 03I_R1 = 12 / 100 = 0.12 A
  4. 04I_R2 = 12 / 200 = 0.06 A

Frequently Asked Questions

Is parallel resistance always less than the smallest?

Yes. Additional paths always reduce total resistance.

What if both resistors are equal?

R_eq = R/2. Two identical resistors in parallel give half the individual value.

How about three in parallel?

Extend: 1/R_eq = 1/R1 + 1/R2 + 1/R3.

Learn More

Guide

Ohm's Law Guide

A complete guide to Ohm's Law. Learn the relationship between voltage, current, and resistance, with practical examples, the power triangle, and circuit analysis tips.

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