Resistors in Series & ParallelFree online science calculator — instant results, no sign-up
Combine two resistors in series and in parallel.
About the Resistors in Series & Parallel
The Resistors in Series & Parallel calculator finds the equivalent resistance of two resistors connected end-to-end in series or across the same two nodes in parallel. Enter both resistance values in ohms to compare the two configurations. With the default inputs of 100 Ω and 200 Ω, the series total is 300 Ω and the parallel total is 66.6667 Ω.
- Resistor 1 (Ω)
- The resistance of the first resistor in ohms (Ω), with a default value of 100.
- Resistor 2 (Ω)
- The resistance of the second resistor in ohms (Ω), with a default value of 200.
Formula and method
Series: R_s = R_1 + R_2. Parallel: R_p = (R_1 × R_2) / (R_1 + R_2). With the defaults: R_s = 100 + 200 = 300 Ω; R_p = (100 × 200) / (100 + 200) = 66.6667 Ω, rounded to four decimal places.
- R_1Resistance of Resistor 1, in ohms (Ω).
- R_2Resistance of Resistor 2, in ohms (Ω).
- R_sEquivalent resistance of the two resistors connected in series, in ohms (Ω).
- R_pEquivalent resistance of the two resistors connected in parallel, in ohms (Ω).
The calculator adds the two resistance values to obtain the series total. For the parallel total, it multiplies the resistance values and divides that product by their sum. Using 100 Ω and 200 Ω, the sum is 300 Ω and the parallel calculation is 20000 / 300 Ω, displayed as 66.6667 Ω.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Resistor 1100 Ω
- Resistor 2200 Ω
Results
- Series total300 Ω
- Parallel total66.6667 Ω
How to use the Resistors in Series & Parallel
- 1Enter the first resistor's resistance in Resistor 1 (Ω), or keep the default of 100.
- 2Enter the second resistor's resistance in Resistor 2 (Ω), or keep the default of 200.
- 3Ensure both entries are expressed in ohms; convert values given in kilohms or megohms before entering them.
- 4Read the series total: the default inputs produce 300 Ω for an end-to-end connection.
- 5Read the parallel total: the default inputs produce 66.6667 Ω when both resistors connect across the same two nodes.
Reading your result
The Series total row gives the resistance seen across the entire end-to-end pair, where the same current passes through both resistors. For the defaults, it is 300 Ω. The Parallel total row gives the resistance seen across the shared nodes, where both resistors have the same voltage across them. For the defaults, it is 66.6667 Ω. For two positive, finite resistances, the series total exceeds either individual resistance, while the parallel total is less than either one. These rows describe alternative wiring configurations, not two results for a single unchanged circuit.
Limitations
The formulas assume ideal resistors with fixed resistance and ideal connecting wires. They do not account for component tolerance, temperature changes, lead resistance, or high-frequency parasitic effects, and they do not calculate current, voltage, power dissipation, or safe power ratings. Positive, finite resistance values are the intended inputs. One ideal zero-ohm resistor makes the parallel equivalent zero if the other resistance is positive; if both inputs are zero, the parallel formula becomes 0/0 and requires special handling, even though the ideal physical equivalent is zero. An open circuit cannot be represented by an ordinary finite resistance entry. Displayed decimal precision does not imply equivalent measurement accuracy.
Common questions
Why is the parallel total 66.6667 Ω when both resistors are at least 100 Ω?+
Parallel wiring provides two paths for current, increasing total conductance. For 100 Ω and 200 Ω, the equivalent resistance is (100 × 200) / (100 + 200) = 66.6667 Ω after rounding, which is below the smaller resistor.
How do I know whether to use the series or parallel output?+
Use the series output when the resistors form one unbranched path so the same current passes through both. Use the parallel output when each resistor connects across the same two nodes so both have the same voltage across them.
Does swapping Resistor 1 and Resistor 2 change either total?+
No. Both addition and multiplication are independent of input order, so swapping 100 Ω and 200 Ω still gives 300 Ω in series and 66.6667 Ω in parallel.
Can I replace the pair with one resistor matching the calculated total?+
An ideal single resistor with the equivalent resistance presents the same resistance at the pair's external terminals. In a real circuit, the replacement must also have suitable tolerance, power and voltage ratings; the calculator does not check these. A replacement also removes any accessible junction between the series resistors.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
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Results are estimates for informational purposes and are not financial, medical or legal advice.