How do you calculate resistors in series?

Add them: Req = R1 + R2 + … + Rn. Convert every value to the same unit first. There is no reciprocal and no division, and the order of the resistors does not matter.

Does the total resistance increase or decrease in series?

It always increases. The series total is larger than the largest single resistor in the chain, because every resistor adds another obstacle to the one path the current has. If your result is smaller, you have applied the parallel rule by mistake.

Is the current the same through resistors in series?

Yes. A series chain has one path, so the same current flows through every resistor in it. What differs is the voltage across each one, which is proportional to its resistance.

How many resistors can you put in series?

Electrically, as many as you like - the formula does not care. Practically, each part adds two solder joints and a tolerance contribution, so chains longer than three or four are usually a sign that a different value or a trimmer would be better.

What is the difference between series and parallel resistance?

Series resistors share one current and add directly, so the total goes up. Parallel resistors share one voltage and combine reciprocally, so the total goes down below the smallest of them. Series divides voltage; parallel divides current.

Series Resistance Calculator · NeoCircuits Lab

Name: Series Resistance Calculator
Author: NeoCircuits Lab

Resistors in series add. The total resistance is the sum of every resistor in the chain, the same current flows through all of them, and the supply voltage divides between them in proportion to each resistance.

Series Resistance Formula

A series chain has exactly one path for current, so the same current I flows through every resistor in it. That single fact is where the whole formula comes from, and it is worth holding on to: series means one current, shared.

Kirchhoff's voltage law says the individual voltage drops around a loop must add up to the voltage applied across it. For three resistors that is:

V = V_{1} + V_{2} + V_{3}

Ohm's law turns each drop into current times resistance. Because the current is the same everywhere, the same I appears in every term:

I \times R_{e q} = I \times R_{1} + I \times R_{2} + I \times R_{3}

Divide through by I and it cancels completely, leaving the resistances adding directly. This is the equivalent series resistance formula, for any number of resistors:

R_{e q} = R_{1} + R_{2} + \dots + R_{n}

Series resistance: the total is the plain sum, with no reciprocals anywhere.

Because the current cancelled, nothing about the supply survives into the answer - which is why the order of the resistors makes no difference at all, and why swapping two of them on a board changes nothing electrically.

How the voltage divides across a series chain

Each resistor takes a share of the supply voltage in proportion to its own resistance. This is the voltage divider rule, and it falls straight out of the same shared current:

V_{k} = V \times \frac{R_{k}}{R_{e q}}

So the largest resistor in a series chain always drops the most voltage and, since power is current times voltage, dissipates the most heat. That is the practical reason to work out the series total before choosing part ratings.

Worked example

Given

R1 = 1 kΩ
R2 = 2.2 kΩ
R3 = 470 Ω

Working

Req = R1 + R2 + R3
Req = 1000 Ω + 2200 Ω + 470 Ω

Answer3.67 kΩ

Note that no standard E24 resistor equals 3.67 kΩ. A series chain is one way to reach a value you cannot buy as a single part.

Why Add Resistors in Series?

Adding resistors in series is the standard way to reach a resistance you cannot buy. Real resistors only come in the IEC 60063 preferred values, so a design calling for 3.67 kΩ has no single part - but 1 kΩ, 2.2 kΩ and 470 Ω in series get there exactly, out of parts most people already have in a drawer.

Spreading heat across more parts

Two 5 kΩ resistors in series make 10 kΩ, and each one now dissipates half the power a single 10 kΩ part would have. Where the total power is close to a resistor rating, splitting it in series is cheaper and more reliable than buying one large part, and it spreads the heat over a larger area of board.

Sharing voltage across more parts

Every resistor has a maximum working voltage as well as a power rating, and a small surface-mount part can be limited to 50 V or less. Two in series each see half the applied voltage, which is how high-voltage dividers are built from ordinary parts.

Tolerance and Accuracy in Series Chains

Series resistors do not just add their values - they add their errors. Three ±1% resistors in series give a total that could be 1% out in the worst case, since every part can drift the same way at once. That worst case is rare; the statistically likely error is the root-sum-square, which for equal tolerances is the tolerance divided by the square root of the number of parts.

Δ_{r s s} = \frac{Δ}{\sqrt{n}}

Likely error across n equal-tolerance parts, as opposed to the worst case.

The practical consequence for anyone building a divider or a reference: a series chain does not improve accuracy over one part of the same tolerance. If you need a precise ratio, buy the tolerance - use the tolerance selector under the results table to see what each grade actually gets you.

Series Resistance in Practice

Current limiting

A resistor in series with an LED, a base, or a gate is the commonest circuit in electronics. The series resistance sets the current, and the calculation is the same sum whether it is one resistor or three in a chain.

Parasitic series resistance you did not add

Track resistance, connector contact resistance, a long test lead and the internal resistance of a battery are all in series with your circuit whether you drew them or not. At low resistances they stop being negligible: 100 mΩ of wiring matters a great deal in a 1 Ω shunt and not at all in a 100 kΩ divider.

Measuring a series total

Measure the chain with nothing else connected. A meter across a series pair that is still soldered into a circuit reads that pair in parallel with everything else on those two nodes, which is almost never the number you wanted.

Common mistakes

Using the reciprocal formula. Reciprocals are for parallel; series is a plain sum. If your answer came out smaller than the largest resistor, you used the wrong rule.
Mixing units before adding. 1 kΩ + 470 Ω is 1.47 kΩ, not 471. Convert everything to ohms first, or let the unit dropdowns do it.
Assuming a series chain is more accurate than one resistor. The tolerances add; the accuracy does not improve.
Forgetting that the largest resistor dissipates the most power, and rating all the parts for the average instead of their actual share.
Measuring the chain in circuit, so the meter reads the chain in parallel with the rest of the board.

Frequently asked questions

How do you calculate resistors in series?: Add them: Req = R1 + R2 + … + Rn. Convert every value to the same unit first. There is no reciprocal and no division, and the order of the resistors does not matter.
Does the total resistance increase or decrease in series?: It always increases. The series total is larger than the largest single resistor in the chain, because every resistor adds another obstacle to the one path the current has. If your result is smaller, you have applied the parallel rule by mistake.
Is the current the same through resistors in series?: Yes. A series chain has one path, so the same current flows through every resistor in it. What differs is the voltage across each one, which is proportional to its resistance.
How many resistors can you put in series?: Electrically, as many as you like - the formula does not care. Practically, each part adds two solder joints and a tolerance contribution, so chains longer than three or four are usually a sign that a different value or a trimmer would be better.
What is the difference between series and parallel resistance?: Series resistors share one current and add directly, so the total goes up. Parallel resistors share one voltage and combine reciprocally, so the total goes down below the smallest of them. Series divides voltage; parallel divides current.

Assumptions and limitations for Series Resistance Calculator are listed on the About page. Every worked example on this site is checked against the same solver the calculator uses.