Equivalent Resistance Calculator
Compute the equivalent resistance of resistors in series or parallel with fully substituted working. Handles 2 to 4 resistors and cross-checks the two-resistor parallel shortcut R₁R₂ ÷ (R₁ + R₂) — handy for physics circuits.
Try an example
Enter the resistance values to see the equivalent resistance (R3 and R4 are optional).
Done
Equivalent Resistance Calculator
How to use
- 1
Pick the connection
Choose series or parallel.
- 2
Enter the resistances
Fill in R₁ and R₂ (plus optional R₃ and R₄).
- 3
Read the result and working
The equivalent resistance appears with the substituted formula, ready to copy.
Features
- Series and parallel equivalents with substituted formula working
- Two to four resistors (R₃ and R₄ optional)
- Two-resistor parallel results cross-checked against R₁R₂ ÷ (R₁ + R₂)
- Non-positive values and skipped R₃ reported as errors; inputs are never transmitted
Use cases
Check circuit homework
Verify hand-worked series and parallel combinations against the shown steps.
Pick parts for projects
See whether combining the resistors on hand reaches a target value.
Set up Ohm’s law
Use the equivalent resistance as the first step before V = RI calculations.
Details
Series resistors add up: R = R₁ + R₂ + …. Parallel resistors combine through reciprocals, 1/R = 1/R₁ + 1/R₂ + …, and for exactly two resistors this rewrites as R = R₁R₂ ÷ (R₁ + R₂). The tool substitutes your values into whichever formula applies.
The direction of each rule matters. Series connections grow the total, while parallel connections shrink it — the equivalent resistance of a parallel group is smaller than every individual resistor. Glancing at whether the result is larger or smaller than the inputs alone catches most formula mix-ups.
Conditions: resistance values must be positive (zero or negative values are unphysical, and zero breaks the parallel division). R₃ and R₄ are optional, and R₄ cannot be used without R₃. Inputs are never transmitted; all computation happens locally in your browser.
FAQ
Why do series and parallel use different formulas?
In series the same current flows through one path, so resistances add (R = R₁ + R₂ + …). In parallel the current splits, so reciprocals add (1/R = 1/R₁ + 1/R₂ + …). A parallel combination is always smaller than every individual resistor.
Can I enter a resistor of 0 Ω in parallel?
No. A 0 Ω resistance is a plain wire, which would force the equivalent resistance to 0. The tool treats anything that is not positive as an error.
Does R₁R₂ ÷ (R₁ + R₂) work for three resistors?
Only for two. Three or more need 1/R = 1/R₁ + 1/R₂ + 1/R₃ + …, which is what the tool uses — it shows the two-resistor shortcut only when exactly two values are entered.
What about circuits mixing series and parallel?
This tool handles one step at a time. Mixed circuits are solved by reducing each group separately — you can use the tool once per group, then combine those results.
Related Tools
Significant Figures Calculator
Count significant figures, round to a chosen precision, and apply the multiplication/division or addition/subtraction rules. Switch between half-up and JIS Z 8401 half-even rounding; scientific notation is shown alongside.
Constant Acceleration
Calculate velocity and displacement from initial velocity, constant acceleration and time, with unit conversion and worked steps.
Trigonometry Calculator
Enter an angle to get sin, cos and tan at once. Special angles like 30°, 45° and 60° are shown as exact values (1/2, √3/2), with degree and radian support, pi expressions such as pi/6, plus the quadrant signs and the reference-angle working.
All processing happens in your browser. Your files are never uploaded.
Verified: Known values (series 9 and 650, parallel 2 and 1), non-positive errors, the skipped-R3 error, the two-resistor shortcut and the English page are covered by browser tests
Did you know?
A parallel combination is always smaller than any single resistor: 3 Ω and 6 Ω in parallel give 2 Ω. The reciprocal-sum formula is exactly that "pulled toward the smaller value" behavior.