Series Resistor Calculator

Background.

Resistors in series add. That single sentence is the whole arithmetic of this page, and it is genuinely that simple — but the reason people reach for a series resistor calculator is almost never the addition. It is one of three follow-up questions that the addition alone does not answer: whether the chain still hits its target once every part is at the wrong end of its tolerance, how much power the chain has to get rid of and which resistor gets the worst of it, and whether the whole exercise is unnecessary because a single stock resistor would land close enough anyway. This calculator answers all four at once.

Enter between two and twenty resistors, the tolerance they share, and the current you expect to push through them. Engineering shorthand works, so 4.7k and 1M are read the way you would say them out loud. The one shorthand deliberately refused is a lower-case m, because it means milli in SI and mega on a hastily drawn schematic, and silently choosing one of those over the other is a factor of a billion. Better to ask.

The physics is Kirchhoff's voltage law. A series chain has exactly one path for current, so the same current flows through every element in it. The voltage dropped across each resistor is that shared current times its own resistance, and the total voltage across the chain is the sum of those drops. Divide both sides by the shared current and the currents cancel, leaving the rule quoted in every circuits text: R_series equals R1 plus R2 plus R3, all the way to Rn. OpenStax states it in exactly that form in University Physics Volume 2, and it is the first reduction taught in MIT's 6.002.

One consequence of that shared current is worth pulling out of the maths, because it decides which part in your chain gets hot. Since every resistor carries the same current, the power each dissipates is I squared times its own resistance — so power splits in exactly the same proportion as resistance does. In a chain of 220 Ω, 330 Ω and 470 Ω, the 470 Ω resistor carries 46 % of the total resistance, drops 46 % of the total voltage and dissipates 46 % of the total heat. The calculator names that resistor and prints its share, because sizing the wattage of the whole chain from the total is a mistake: it is the dominant resistor that decides whether a quarter-watt part will do.

The tolerance result contains the page's most useful counter-intuitive fact. Adding three ±5 % resistors does not give you a ±15 % chain. If every resistor shares the same tolerance t, then the worst-case total is the sum of every value at (1 − t), which factorises straight back to (1 − t) times the nominal total. The percentage is unchanged. What does grow is the absolute window: ±5 % of 1,020 Ω is ±51 Ω where ±5 % of 220 Ω is only ±11 Ω. So a series chain does not degrade your accuracy in relative terms, which is a real reason to prefer it over other ways of hitting an awkward value. This holds only when the parts genuinely share a tolerance; mix a ±1 % part with a ±10 % part and the chain's window has to be worked out term by term.

Finally, the stock-value check exists because the honest answer to a lot of series-resistor questions is "do not bother". IEC 60063 defines the E24 series of twenty-four values per decade that ±5 % resistors are made in, and the E96 series of ninety-six values that ±1 % parts are made in. If your carefully summed 16.2 kΩ is within 1.2 % of a stock 16 kΩ, and you are using ±5 % parts, the chain is buying you nothing but two extra solder joints and two extra things to go wrong. The calculator tells you the nearest value in both series and the error each would introduce, so you can make that call with a number rather than a hunch.

One scope limit, stated up front: this is a DC and low-frequency model. It ignores the lead inductance and end-to-end capacitance that make a long chain of resistors behave differently at radio frequencies, and it ignores the way each resistor's value drifts with its own temperature once it is dissipating power.

What is series resistor calculator?

A series connection is one in which components are joined end to end so that there is exactly one path for current. Every element in the chain therefore carries the identical current — not a similar current, the same one — and that constraint is what produces every result on this page.

Because the current is shared, Ohm's law gives the voltage across each resistor as V_i = I x R_i. Kirchhoff's voltage law says the drops around the loop must sum to the applied voltage, so V_total = I x R1 + I x R2 + … + I x Rn = I x (R1 + R2 + … + Rn). Comparing that with V_total = I x R_series identifies the equivalent resistance of the chain as the plain sum of its parts.

That result has three practical corollaries. The total is always larger than the largest single resistor in the chain, which is why series connection is the way to make a bigger value out of smaller ones. The voltage divides in proportion to resistance, which is the basis of the voltage divider. And the power divides in the same proportion, because P_i = I² x R_i with I common to all of them.

Series chains are used to reach a value that is not manufactured, to spread heat across several physically small parts instead of one large one, and to raise the voltage a string can withstand — three 200 V-rated resistors in series share the applied voltage and can stand roughly three times as much across the chain as one alone. They are not a way to improve precision: the relative tolerance of the chain is the relative tolerance of the parts.

How to use this calculator.

1. 01Type the resistors into the list, separated by commas. Use the values printed on the parts, not the values you measured — the tolerance window below is what turns nominal values into a real range.
2. 02Use engineering shorthand if it is quicker: 4.7k, 10K, 1M and 2.2G are all read correctly. Write 0.001 rather than 1m; a lower-case m is refused rather than guessed at.
3. 03Set the tolerance to the one your parts share — 5 for a gold band, 1 for brown, 2 for red. If your chain mixes tolerances, run it once at the loosest value to get a conservative window.
4. 04Enter the current you expect through the chain, in amperes. Twenty milliamps is 0.02. If you do not know it yet, leave it at the default and come back once the rest of the circuit is settled — the resistance results do not depend on it.
5. 05Read the total, then immediately read the worst-case low and high beside it. If your circuit only works between two limits, those are the two numbers that have to fit, not the nominal total.
6. 06Check which resistor dominates. In series it takes the largest share of voltage and heat, so it is the one whose power rating you have to size first.
7. 07Read the stock-value line before you build anything. If a single E24 or E96 resistor lands inside your tolerance, use it — fewer parts, fewer joints, less to go wrong.
8. 08If the power figure is more than about half of your resistors' combined rating, size up. Rated dissipation on a resistor datasheet is quoted at an ambient temperature — commonly 70 °C — and falls away above it.

The formula.

The series rule follows from one constraint and one law. The constraint is that a series path has no branches, so the current I is identical in every element. The law is Kirchhoff's voltage law: around any closed loop, the sum of the voltage drops equals the sum of the sources.

Apply Ohm's law to each resistor: V₁ = I·R₁, V₂ = I·R₂, and so on. Sum them: V_total = I·R₁ + I·R₂ + … + I·Rₙ. Factor out the common current: V_total = I·(R₁ + R₂ + … + Rₙ). Since by definition V_total = I·R_series, the equivalent resistance is R_series = R₁ + R₂ + … + Rₙ. Nothing is approximated and no ordering matters, which is why shuffling the chain changes nothing.

The dissipation results come from the same shared current. Total power is P = I²·R_series, and each resistor's own share is P_i = I²·R_i, so P_i / P = R_i / R_series. Power divides in exactly the same ratio as resistance. That is why this page names the largest resistor and prints one percentage that simultaneously describes its share of the resistance, of the voltage and of the heat.

The tolerance window assumes every resistor carries the same fractional tolerance t. The worst-case low total is Σ Rᵢ(1 − t), which factorises to (1 − t)·Σ Rᵢ, and the worst-case high is (1 + t)·Σ Rᵢ. The relative window is therefore exactly t, unchanged by the number of resistors — the chain is no less accurate, in percentage terms, than a single part would be. This is a statement about the worst case, not a statistical one; if the parts are independently distributed the realistic spread is narrower still, but that is a manufacturing-distribution argument the datasheet does not guarantee.

Rounding happens once, at the end. Every intermediate step is exact decimal arithmetic at forty significant digits, so 0.1 + 0.2 comes back as 0.3 rather than 0.30000000000000004, and the returned numbers are rounded to ten decimal places only as they cross the boundary out of the calculator. The stock-value comparison is made against the unrounded total, using exact integer mantissas from the E24 and E96 tables, so it cannot be thrown off at a boundary by floating-point error.

A worked example.

Frequently asked questions.

References& sources.

1. [1]OpenStax (Rice University), "University Physics Volume 2", §10.2 "Resistors in Series and Parallel". Equation 10.2 states the series rule as R_S = R1 + R2 + R3 + … + R(N−1) + R_N = Σ Ri, derived from the common current and Kirchhoff's voltage law; the same section gives the per-resistor power split and notes that total dissipated power is the sum of the individual dissipations. Retrieved and read 2026-07-29.
2. [2]"Series and parallel circuits", reference article, retrieved and read 2026-07-29. The independent second statement of the rule used to check this page: R = Σ Ri = R1 + R2 + R3 + ⋯ + Rn for a series connection, against the reciprocal-sum form for a parallel one. Agrees with OpenStax Equation 10.2 term for term.
3. [3]IEC 60063:2015, "Preferred number series for resistors and capacitors", third edition, 27 March 2015. Defines the E24 (±5 %) and E96 (±1 %) value sets this page's nearest-stock-value check tests against, and the tolerance each series pairs with. Retrieved 2026-07-29 via the reference summary of the series values and their standard tolerances.
4. [4]Vishay Draloric / Beyschlag / BCcomponents, "Resistor Color Card", document VMN-MS6212-1501 (2015). Prints the full E24, E96 and E192 tables under the heading "According to IEC 60063"; the ninety-six E96 mantissas used by this calculator were transcribed from it directly on 2026-07-29.
5. [5]Vishay BCcomponents, "MRS16, MRS25 Professional Thin Film Leaded Resistors", document 28724, revision 07-Mar-16. Source of the voltage- and power-rating figures quoted on this page: rated dissipation P70 of 0.4 W (MRS16) and 0.6 W (MRS25) — that is, rated at 70 °C ambient — maximum operating voltage 200 V and 350 V respectively, and a peak permissible film temperature of 155 °C. Retrieved and read 2026-07-29.
6. [6]Vishay, "D/CRCW e3 Standard Thick Film Chip Resistors", document 20035, revision 14-Apr-2026. Confirms the same rating convention on surface-mount parts — rated dissipation quoted as P70, permissible film temperature 155 °C, maximum operating voltage rising from 75 V on an 0402 to 500 V on a 2512 — which is the basis for the voltage-sharing answer in the FAQ. Retrieved and read 2026-07-29.