100 Ω, 220 Ω, and 330 Ω
R = R₁ + R₂ + R₃
The total is 100 + 220 + 330 = 650 Ω. Every positive resistor added in series increases the equivalent resistance.
Series & parallel circuits
Resistor Calculator
Find equivalent resistance for a group of resistors connected in series or in parallel.
Calculate equivalent resistance
Equivalent resistance
Enter at least two resistors, then select Calculate.
- In ohms
- Connection
- Formula
Calculation steps and exact value
Exact resistance in ohms:
≈ marks display rounding. Calculations run in your browser. Press Enter to calculate. Successful results appear in this tab's Recent calculations.
Equivalent resistance examples
100 Ω and 300 Ω
R = (R₁ × R₂) ÷ (R₁ + R₂)
For two positive resistors, the product-over-sum shortcut gives 30,000 ÷ 400 = 75 Ω. This is below either branch's resistance.
1 kΩ and 500 Ω in parallel
R = 1 ÷ (1/1,000 + 1/500)
The exact result is 1,000/3 Ω. At two decimal places it displays ≈ 333.33 Ω, or ≈ 0.33 kΩ. The selected unit affects visible rounding.
Input rules and the ideal-resistor model
Enter 2 to 10 nominal resistor values for one series group or one parallel group. The calculator does not infer a circuit from a schematic or solve a network containing both connection types. Values must be finite and nonnegative. Open circuits, infinity, negative resistance, expressions, and scientific notation are not accepted.
The exact unit factors are 1 kΩ = 1,000 Ω and 1 MΩ = 1,000,000 Ω. Each numeric input allows up to 64 characters, 15 integer digits, and 10 decimal places. A zero-ohm resistor adds nothing in series. In parallel, a zero-ohm branch connects the group's endpoints directly in this ideal model, giving zero equivalent resistance.
All unit conversions, sums, and reciprocals retain exact fractions. Only the final display is rounded, with halfway values rounded away from zero and trailing zeros omitted. ≈ identifies a rounded display. A positive result that rounds to zero has a separate notice. The exact fraction in ohms is available in the calculation details.
This tool models ideal resistors using the values entered. It does not estimate tolerance, temperature changes, wiring resistance, AC impedance, power ratings, or source current. Equivalent resistance alone does not determine which physical components are suitable for a circuit.
Changing the result unit or decimal places reformats the same exact result without adding a recent-calculation entry. Editing a resistance, unit, connection, or row count hides the previous result until you calculate again.
Formula reference: OpenStax University Physics Volume 2 — Resistors in Series and Parallel.
Common questions
Why is parallel resistance smaller than either resistor?
For positive, finite branch resistances, an additional parallel branch provides another path between the same endpoints. The equivalent resistance is below the smallest branch resistance. If all n branches have the same resistance R, the equivalent resistance is R/n.
Can I combine series and parallel groups?
Reduce each identifiable group separately, then use its equivalent resistance in the next group. This form handles only one connection type at a time. Copying a rounded decimal into another calculation can introduce rounding error, so use an exact value when available or sufficient precision for your purpose. Some networks cannot be reduced using only series and parallel groups.
Does a zero-ohm result mean no current flows?
No. Zero resistance represents an ideal short circuit. Current then depends on the source and other resistance in the complete circuit, which this tool does not model. An open circuit is a different case and is not an input option here.
Does the resistor order change the result?
No. Within a single series group or a single parallel group, rearranging the entered values leaves the equivalent resistance unchanged. Changing the connection type generally changes the result.