Parallel & Series Resistor Calculator — Total R
Equivalent resistance for series, parallel & mixed networks
Required Parameters
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Quick Answer
Series resistors add (R = R1 + R2 + …). Parallel resistors: 1/R = 1/R1 + 1/R2 + … — for two resistors use (R1×R2)/(R1+R2).
Parallel & Series Resistor Calculator — Engineering Guide
Use this parallel resistor calculator and series resistor calculator to find the equivalent resistance of resistors connected in series, parallel, or mixed configurations. Enter comma-separated values (e.g., 1k, 4.7k, 10k) and get total resistance instantly.
Parallel Resistor Calculator
Resistors in parallel share the same two nodes. Current splits among branches; total resistance is always less than the smallest individual value.
1/Rtotal = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn
For exactly two resistors, use the product-over-sum shortcut:
Rtotal = (R1 × R2) / (R1 + R2)
Example — Parallel Resistor Calculator
Two resistors in parallel: 100 Ω ∥ 200 Ω
Rtotal = (100 × 200) / (100 + 200) = 66.7 Ω
Series Resistor Calculator
Resistors in series carry the same current. Voltages add across each element; total resistance is always greater than the largest individual value.
Rtotal = R1 + R2 + R3 + ... + Rn
Example — Series Resistor Calculator
Three resistors in series: 100 Ω + 220 Ω + 330 Ω
Rtotal = 100 + 220 + 330 = 650 Ω
Series Parallel Circuit Calculator
For mixed networks, simplify inner groups first, then work outward:
- Identify purely series or parallel sections
- Replace each group with its equivalent resistance
- Repeat until one total remains
Example: R1 = 1 kΩ in series with (R2 = 2.2 kΩ ∥ R3 = 4.7 kΩ)
- Parallel group: (2200 × 4700) / (2200 + 4700) = 1497 Ω
- Series total: 1000 + 1497 = 2497 Ω ≈ 2.5 kΩ
Series Resistors
Resistors in series add directly:
Rtotal = R1 + R2 + R3 + ... + Rn
- The same current flows through all resistors
- Voltage is divided across each resistor
- Total resistance is always greater than the largest individual resistor
Example
Three resistors in series: 100 Ω + 220 Ω + 330 Ω
Rtotal = 100 + 220 + 330 = 650 Ω
Parallel Resistors
Resistors in parallel combine using the reciprocal formula:
1/Rtotal = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn
For two resistors, a simpler product-over-sum formula:
Rtotal = (R1 × R2) / (R1 + R2)
- The same voltage appears across all resistors
- Current is divided among branches
- Total resistance is always less than the smallest individual resistor
Example
Two resistors in parallel: 100 Ω ∥ 200 Ω
Rtotal = (100 × 200) / (100 + 200) = 66.7 Ω
Special Cases
Equal Parallel Resistors
For N identical resistors of value R in parallel:
Rtotal = R / N
Examples:
- Two 1 kΩ in parallel = 500 Ω
- Three 1 kΩ in parallel = 333 Ω
- Four 1 kΩ in parallel = 250 Ω
Getting Non-Standard Values
When you need a value that doesn't exist in standard E24/E96 series, combine resistors:
- Need 750 Ω? → 1.5 kΩ ∥ 1.5 kΩ, or 330 Ω + 420 Ω in series
- Need 15 kΩ? → 10 kΩ + 4.7 kΩ in series (≈ 14.7 kΩ)
- Need 3.3 kΩ? → 10 kΩ ∥ 4.7 kΩ (≈ 3.2 kΩ)
Power Dissipation
In series: the resistor with the highest value dissipates the most power (P = I²R, same I).
In parallel: the resistor with the lowest value dissipates the most power (P = V²/R, same V).
Always verify that each individual resistor can handle its share of the power dissipation.
Mixed Configurations
For complex circuits:
- Identify series and parallel groups
- Simplify the innermost groups first
- Work outward until you reach a single equivalent resistance
Tolerance Considerations
Combined tolerance is worse than individual tolerances:
- Two 5% resistors in series → worst case: ±5% total
- Two 5% resistors in parallel → worst case: ±5% total
- For precision, use 1% or better resistors
Related Tools
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- Resistor Color Code Guide — Chart, mnemonic & tolerance explained
Design Notes
Combining resistors is an invaluable trick in professional prototyping. When you don't have the exact E96 precision value needed for an Op-Amp gain stage, you can parallel two higher-value resistors to hit the exact target. Furthermore, dropping high voltages or handling high power (e.g., snubber circuits) is often better done by stringing multiple smaller 1/4W resistors in series, which spreads the heat and significantly increases the maximum voltage rating (dielectric breakdown limits).
Common Mistakes
- 1
Thinking parallel resistors can increase the total resistance. Adding a resistor in parallel ALWAYS decreases the equivalent resistance.
- 2
Ignoring the power rating split. If 1W is flowing into two unequally sized parallel resistors, the lower resistance one takes the majority of the heat.
- 3
Failing to account for parasitic inductance when placing wirewound resistors in parallel for high-frequency RF dummy loads.
Engineering Handbox
1. Two-resistor shortcut: R = (R1 × R2) / (R1 + R2) 2. R = (10000 × 4700) / (10000 + 4700) 3. R = 47,000,000 / 14,700 = 3197.9 Ω
Knowledge Base
What is a parallel resistor calculator?
A parallel resistor calculator finds the equivalent resistance when two or more resistors share the same two nodes. Enter your values (e.g., 1k, 4.7k, 10k) and get the total instantly. For two resistors use R = (R1 × R2) / (R1 + R2). The result is always less than the smallest individual resistor.
What is a series resistor calculator?
A series resistor calculator adds resistor values in a single current path: R_total = R1 + R2 + R3 + ... + Rn. Example: 100 Ω + 220 Ω + 470 Ω = 790 Ω. Series combinations are used for voltage division, current limiting, and reaching non-standard E-series values.
How do I calculate a series parallel circuit?
Break the circuit into groups: simplify the innermost parallel or series section first, then work outward. Example: R1 in series with (R2 ∥ R3): first R_parallel = (R2 × R3)/(R2 + R3), then R_total = R1 + R_parallel. Label each step on a sketch before entering values.
How do I calculate total resistance in series?
Simply add all resistor values together: R_total = R1 + R2 + R3 + ... + Rn. For example, three resistors of 100, 220, and 470 ohms in series give 790 ohms. The total is always larger than the largest individual resistor. Current through all series resistors is the same, but each drops a proportional voltage.
What is the formula for parallel resistors?
The reciprocal of the total resistance equals the sum of reciprocals: 1/R_total = 1/R1 + 1/R2 + ... + 1/Rn. The result is always smaller than the smallest individual resistor. For two resistors, use the shortcut: R_total = (R1 x R2) / (R1 + R2).
What is the shortcut formula for two parallel resistors?
For exactly two resistors in parallel: R_total = (R1 x R2) / (R1 + R2). This is called the product-over-sum method. Example: 10k and 4.7k in parallel = (10000 x 4700) / (10000 + 4700) = 47000000 / 14700 = 3197 ohms (approximately 3.2k). This shortcut only works for exactly two resistors.
What happens when I put identical resistors in parallel?
N identical resistors of value R in parallel give R_total = R / N. Two 10k resistors in parallel = 5k. Three 10k resistors in parallel = 3.33k. Ten 10k resistors in parallel = 1k. This is useful for increasing power handling: ten 1/4W 10k resistors in parallel can handle 2.5W total while giving 1k equivalent.
Does adding a resistor in parallel increase or decrease total resistance?
Adding a resistor in parallel ALWAYS decreases the total resistance, no matter how large the added resistor is. Even adding a 10M resistor in parallel with a 100 ohm resistor reduces the total slightly (to 99.999 ohms). This is because you are providing an additional path for current to flow, which by definition reduces total opposition.
How does power distribute in parallel resistors?
In a parallel circuit, voltage across all resistors is the same, but current splits inversely with resistance. Power in each resistor: P = V squared / R. The LOWER value resistor dissipates MORE power. Example: 1k and 10k in parallel across 10V: the 1k dissipates 100mW while the 10k only dissipates 10mW. Always check that each resistor can handle its individual power share.
How do I calculate a mixed series-parallel network?
Break the circuit into groups: first identify purely series or purely parallel sections. Simplify the innermost groups first, then work outward. For example, R1 in series with (R2 parallel R3): first calculate R_parallel = (R2 x R3)/(R2 + R3), then R_total = R1 + R_parallel. Draw the circuit and label each step.
How do I hit an exact resistor value not in the E-series?
Use two resistors: (1) Series: to get values between standard values, add a small resistor in series (e.g., 4.7k + 330 = 5.03k). (2) Parallel: to get values below standard, parallel two larger values (e.g., 10k parallel 15k = 6k). There are online calculators that find the best E24 or E96 pair to match any target value.
Does tolerance stack up in series or parallel?
In series, the absolute tolerance error can accumulate (worst case adds up). In parallel, the relative tolerance effect is reduced through averaging. For example, two 5% 10k resistors in parallel will have an equivalent tolerance closer to 3.5% rather than 5%, because individual errors partially cancel. This makes parallel combinations more precise than series.
When should I use series resistors instead of a single higher value?
Use series resistors when: (1) You need a non-standard value not in your kit. (2) High voltage applications: each resistor only sees a fraction of the total voltage, staying within its dielectric rating. (3) Power spreading: distributing heat across multiple packages. (4) PCB layout: sometimes two 0603 resistors fit better than one large package.
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