Resistor Series & Parallel Calculator
Calculate equivalent resistance for resistors in series, parallel, or mixed configurations. Add or remove resistors dynamically and see the result instantly.
R_total = R₁ + R₂ + … + Rₙ
Equivalent Resistance (series)
320 Ω
Nearest E12 standard value: 330 Ω
All calculations run live in your browser. Up to 10 resistors supported.
What Is the Resistor Series & Parallel Calculator?
This calculator finds the equivalent resistance for up to 10 resistors in series or parallel. Add resistors dynamically, provide a supply voltage to see per-resistor current and power, and compare the result to the nearest E12 standard value.
- ›Series: same current flows through each resistor, voltages add up
- ›Parallel: same voltage across each resistor, currents add up
- ›Parallel resistance is always less than the smallest individual resistor
- ›Nearest E12 value helps you select a real stock component
Formula
Combination Formulas
Series
R_total = R₁ + R₂ + … + Rₙ
Parallel
1/R_total = 1/R₁ + 1/R₂ + … + 1/Rₙ
2 parallel
R_total = (R₁ × R₂) / (R₁ + R₂)
Current (V known)
I = V / R_total
Power
P = V² / R = I²R = VI
E12 nearest
Snap to standard series value
How to Use
- 1Select Series or Parallel mode using the toggle buttons
- 2Enter a resistor value and unit (Ω, kΩ, MΩ), then press + to add it
- 3Repeat for each resistor, up to 10 total; remove any with the × button
- 4Optionally enter supply voltage to see current and power per resistor
- 5The equivalent resistance and nearest E12 value update automatically
Example Calculation
Three resistors in parallel: 100 Ω, 220 Ω, 470 Ω:
1/R = 0.01000 + 0.00455 + 0.00213 = 0.01667
R = 1/0.01667 = 59.97 Ω
Nearest E12 = 56 Ω or 68 Ω
At 9 V: I_total = 9/59.97 = 150.1 mA
I₁=90mA (100Ω) · I₂=40.9mA (220Ω) · I₃=19.1mA (470Ω)
Two equal resistors in parallel
Two equal resistors R in parallel always give R/2.
E.g., 220 Ω ‖ 220 Ω = 110 Ω. Three give R/3 = 73.3 Ω.
Understanding Resistor Series & Parallel
Resistor Combination Reference
| Configuration | Formula | Key Property |
|---|---|---|
| Series (n) | R = R₁+R₂+…+Rₙ | R > largest Rᵢ |
| Parallel (n) | 1/R = Σ(1/Rᵢ) | R < smallest Rᵢ |
| 2 parallel | R = R₁R₂/(R₁+R₂) | Product over sum |
| n equal R | R_total = R/n | Only for identical R |
| Voltage divider | V_out = V × R₂/(R₁+R₂) | Series, output at R₂ |
Frequently Asked Questions
Why is parallel resistance always less than the smallest resistor?
Conductance G = 1/R adds in parallel: G_total = G₁ + G₂ + … Therefore R_total = 1/G_total is always smaller than any single 1/Gᵢ = Rᵢ.
- ›100 Ω ‖ 1 MΩ ≈ 99.99 Ω, the 1 MΩ barely changes things
- ›100 Ω ‖ 100 Ω = 50 Ω, equal resistors halve the resistance
- ›Adding a short circuit (0 Ω) in parallel gives 0 Ω total
- ›This is why parallel paths are used for current splitting
What is the E12 series?
The E-series ensures that consecutive values in the same decade overlap within manufacturing tolerance. E12 for ±10%, E24 for ±5%, E96 for ±1%.
- ›E12: 12 values per decade, e.g., 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82
- ›E24: 24 values per decade, commonly available in ±5% (gold band)
- ›E96: 96 values per decade, 1% precision resistors
- ›Always pick the nearest E-series value for a practical circuit design
How do I calculate power dissipated in each resistor?
Power determines the wattage rating needed. Exceed a resistor's rated power and it will overheat and fail.
- ›Series: P_i = I² × R_i (same current I through all)
- ›Parallel: P_i = V² / R_i (same voltage V across all)
- ›Always choose a resistor rated at 2× the calculated power for safety
- ›Common ratings: ⅛W, ¼W, ½W, 1W, 2W, 5W
What is a voltage divider?
A resistor divider is the simplest circuit for reducing voltage. The output is taken from the junction of two series resistors.
- ›V_out = V_in × R₂/(R₁+R₂), only valid with high-impedance load
- ›R₁=10kΩ, R₂=10kΩ: V_out = 50% of V_in
- ›Loading effect: a low-impedance load reduces V_out below the formula
- ›Buffer with an op-amp to avoid loading if driving a low-impedance circuit
How do I handle mixed series-parallel circuits?
Complex networks are solved by repeatedly simplifying recognizable series or parallel sub-groups until one equivalent resistance remains.
- ›Draw the circuit and identify series groups (sharing the same current)
- ›Identify parallel groups (sharing the same two nodes)
- ›Replace each group with its equivalent using this calculator
- ›Redraw and repeat until one resistance remains
What is the difference between resistance and impedance?
At DC (0 Hz), impedance = resistance. At higher frequencies, capacitors and inductors contribute frequency-dependent reactance that adds to (or offsets) resistance.
- ›Capacitor: X_C = 1/(ωC), decreases with frequency
- ›Inductor: X_L = ωL, increases with frequency
- ›Z = √(R² + X²), magnitude of impedance
- ›This calculator is for pure resistance (DC or resistive AC only)
Can I use this for LED current-limiting resistors?
LEDs require a current-limiting resistor to prevent thermal runaway. The resistor drops the voltage difference between supply and LED forward voltage.
- ›R = (V_supply − V_forward) / I_LED
- ›Typical V_forward: red/yellow ≈ 2V, green/blue ≈ 3.2V, white ≈ 3.3V
- ›Typical LED current: 20 mA standard, 350 mA–1A for high-power LEDs
- ›Enter the calculated R here to find the nearest E12 standard value