Series & Parallel Resistor Calculator
Combine parts, solve whole networks and make odd values from two standard parts.
How it was calculated
Voltage, current and power in each resistor
Nearest standard values to the total
| Series | Nearest value | Error | Below / above |
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Make a value from standard parts
| Parts | Result | Error |
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| Parts | Result | Error |
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Crystal load capacitors
For the two capacitors of a Pierce crystal oscillator: CL = C1·C2 / (C1 + C2) + Cstray.
Frequency error estimate (optional)
Both are in the crystal datasheet. The estimate uses Δf = fs·C1 / (2(C0 + CL)) from Microchip AN826.
| Capacitors | CL | CL error | Δf |
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About the Series & Parallel Resistor Calculator
Work out the total of any number of resistors, capacitors or inductors connected in series or in parallel, or type a whole network — 10k + (4.7k || 2.2k) — and get the equivalent value with every step shown. Values can be typed the way they are printed: 4.7k, 4k7, 470R, 100n, 2u2.
Two extra panels solve everyday design problems. Make a value finds the single standard (E6 to E192) value closest to a target and the best pairs of standard parts in series and in parallel — 5 kΩ, for example, is exactly 10 kΩ ‖ 10 kΩ or 3 kΩ + 2 kΩ. The crystal load capacitor panel sizes the two capacitors of a quartz-crystal oscillator from the crystal’s load capacitance.
How to use it
- Choose Resistors, Capacitors or Inductors, then Series, Parallel or Network.
- For series or parallel, type the values (add as many rows as you need; each row has its own unit). For a network, type it with + for series and || (or //) for parallel; brackets group parts, and || binds tighter than +.
- Read the total, the steps, and — for resistors and capacitors — how a voltage or current you enter is shared between the parts.
- To hit a value you cannot buy, enter it under Make a value from standard parts, pick the series you stock (E12, E24, E96 …) and compare the best series and parallel pairs.
Examples
10k, 4.7k, 2.2k
16.9 kΩ
10k ‖ 4.7k ‖ 2.2k
1.303 kΩ (1 ÷ (1/10k + 1/4.7k + 1/2.2k))
10k + (4.7k || 2.2k)
10 kΩ + 1.499 kΩ = 11.5 kΩ
1 µF and 2 µF in series on 30 V
667 nF; 20 V across the 1 µF, 10 V across the 2 µF
target 5k, E24
10k ‖ 10k, 7.5k ‖ 15k, 3k + 2k or 4.7k + 300 — all exact
CL 18 pF, stray 5 pF
C1 = C2 = 26 pF exactly; 27 pF (E12) gives 18.5 pF
The formulas
- Resistors and inductors in series add: R = R1 + R2 + …
- Resistors and inductors in parallel add as reciprocals: 1/R = 1/R1 + 1/R2 + …; for two parts R = R1·R2 / (R1 + R2).
- Capacitors are the other way round: in parallel C = C1 + C2 + …, in series 1/C = 1/C1 + 1/C2 + ….
- The total of resistors in parallel is always below the smallest one; capacitors in series give less than the smallest capacitor.
- Inductors are taken as uncoupled: wound close together, their magnetic fields interact (mutual inductance) and change the total.
Sharing voltage and current
Enter a voltage or current to see each part’s share. Resistors in series share the voltage in proportion to their values and carry the same current; in parallel they share the current in inverse proportion. Power per resistor (I²R) tells you the wattage each needs. For ideal capacitors charged from zero, series capacitors share the voltage in inverse proportion to their capacitance (the smallest gets the most); in a real series string, leakage decides the long-term DC sharing, which is why high-voltage banks use balancing resistors.
Making a value from two standard parts
Resistors and capacitors are made in the preferred values of IEC 60063. For a value outside the series, the calculator tries every standard value as the first part and the standard values either side of the exact second part, in series and in parallel, and lists the closest results with their errors. A parallel pair is handy for trimming down; a series pair for adding a small value. Keep the tolerance in mind: two ±1% resistors still give a ±1% result, so an error far below 1% is usually not worth chasing.
Crystal load capacitors
A crystal is cut to oscillate at its marked frequency when it sees a specific load capacitance CL (from its datasheet). In the usual Pierce oscillator the two capacitors C1 and C2 appear in series, plus the stray capacitance of the board and the chip’s pins: CL = C1·C2 / (C1 + C2) + Cstray, so equal capacitors are C = 2 × (CL − Cstray). Microchip AN826 suggests assuming 2 to 5 pF of stray capacitance; your MCU’s datasheet may give its pin capacitance. If you enter the crystal’s shunt (C0) and motional (C1) capacitance, the calculator estimates how far the frequency moves when the real load differs from CL.
Sources
- IEC 60050-131, International Electrotechnical Vocabulary — Circuit theory (series and parallel connection)
- IEC 60063:2015, Preferred number series for resistors and capacitors
- ST AN2867, Guidelines for oscillator design on STM8AF/AL/S and STM32 MCUs/MPUs (CL = CL1·CL2/(CL1 + CL2) + Cs)
- Microchip AN826, Crystal Oscillator Basics and Crystal Selection for rfPIC™ and PICmicro® Devices (CL = C2·C3 / (C2 + C3) + CS, stray capacitance 2–5 pF, shunt capacitance C0 3–7 pF, pulling Δf = fs·C1 / (2(C0 + CL)))
Limitations
- Parts are ideal: no tolerance, temperature coefficient, lead resistance or parasitic inductance and capacitance. At high frequencies a resistor or capacitor no longer behaves as its nominal value.
- Inductors are assumed not to be magnetically coupled; coupled inductors need their mutual inductance, which this calculator does not include.
- The pair search looks at pairs only (not three or more parts) within the series you choose.
- The crystal panel covers the common two-capacitor Pierce oscillator; follow your crystal and MCU makers’ guidance for drive level and oscillation margin.
Privacy
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Frequently asked questions
How do I calculate resistors in parallel?
Add the reciprocals and take the reciprocal of the sum: 1/R = 1/R1 + 1/R2 + …. For two resistors this is R1·R2 / (R1 + R2) — 4.7 kΩ and 2.2 kΩ give 1.499 kΩ. Two equal resistors in parallel give half the value.
Why do capacitors add the opposite way to resistors?
In parallel, capacitors simply add plate area, so the capacitances add. In series, the same charge sits on each one and the voltages add, which makes the reciprocals add: 1/C = 1/C1 + 1/C2. Resistors add in series because their voltages add for the same current.
How do I type a network?
Use + for series and || for parallel, with brackets for groups: 100 + (220 || 330) + 47 is 279 Ω. || binds tighter than +, like × before + in arithmetic, so 10k + 4.7k || 2.2k means 10k + (4.7k || 2.2k).
How can I make a resistor value I do not have?
Enter it under Make a value from standard parts and pick the series you have (E12 for a basic kit, E24 for 5% parts). The calculator lists the best series and parallel pairs and how far each is from the target.
What load capacitors does my crystal need?
Take CL from the crystal datasheet, estimate the stray capacitance (often 2–5 pF), and use C1 = C2 = 2 × (CL − Cstray). For CL = 18 pF and 5 pF stray that is 26 pF; the nearest E12 value, 27 pF, gives 18.5 pF.