What is the formula for resistors in series?

The total resistance is simply the sum of all individual values: Rt = R1 + R2 + ... + Rn. Current is the same through every element; voltage distributes in proportion to resistance.

How is voltage distributed in a series circuit?

Each resistor drops a fraction of the supply proportional to its resistance. The drop across resistor Ri is Vi = I × Ri = V_supply × (Ri / Rt). The drops always sum back to the supply voltage — this is Kirchhoff''s Voltage Law.

How is power dissipation calculated per resistor?

Power for each resistor uses Pi = I² × Ri (or equivalently Vi² / Ri). A resistor with twice the resistance dissipates twice the power at the same current. Always check that the calculated power is within the component's rated wattage (e.g. 0.25 W for a standard ¼ W resistor).

Why is the current identical through every series resistor?

In a series circuit there is only one path for current to flow. Every coulomb that passes through R1 must also pass through R2, R3, and so on — there is nowhere else for it to go. This contrasts with parallel circuits where current splits.

What is a voltage divider and how does it relate?

A voltage divider is simply two (or more) resistors in series used to produce a fraction of the supply voltage at their junction. The output voltage across R2 is V_out = V_in × R2 / (R1 + R2). This calculator shows that drop directly in the per-resistor table.

How do I check whether a resistor will overheat?

The tool shows each resistor's power in watts, milliwatts, or microwatts. Compare that figure against the component's power rating. The most common through-hole resistors are rated ¼ W (250 mW); SMD resistors range from 1/16 W (62.5 mW) upward. Add at least a 50 % safety margin in practice.

Completely. All calculations run in your browser using JavaScript. No values are ever sent to a server.

Resistor Series Calculator

A series resistor calculator that goes beyond a simple sum. Enter any number of resistor values, optionally supply a source voltage or current, and the tool instantly returns the total resistance, the circuit current, and a per-resistor breakdown showing each component’s voltage drop, power dissipation, and its proportional share of the total resistance. Useful for electronics design, circuit homework, voltage-divider sizing, and power-budget checks.

How it works

In a series circuit every resistor is connected end-to-end along a single path, so current has nowhere to branch. The governing equations come directly from Ohm’s law and Kirchhoff’s Voltage Law (KVL):

Rₜ = R₁ + R₂ + ⋯ + Rₙ (total resistance = arithmetic sum)

I = V ÷ Rₜ (one current for the whole loop)

Vᵢ = I × Rᵢ (voltage drop proportional to each Rᵢ)

Pᵢ = I² × Rᵢ (power dissipated by each resistor)

The calculator first sums all the resistors to get Rₜ. If you supply a source voltage V it applies I = V / Rₜ; if you supply a current I it applies V = I × Rₜ. It then sweeps through every resistor to compute the individual voltage drop and power, and cross-checks that KVL holds: the sum of all individual drops must equal the supply voltage, which it always does by construction.

The resistance share column (% of Rₜ) is a quick diagnostic: a resistor dominating the total also dominates the voltage and power. Conversely, small resistors in a high-value series chain have negligible effect and could be omitted.

Worked example

Suppose you have four resistors — 100 Ω, 220 Ω, 470 Ω and 1 000 Ω — wired in series across a 12 V supply:

Step 1 — total resistance

Rₜ = 100 + 220 + 470 + 1000 = 1790 Ω

Step 2 — circuit current (Ohm’s law)

I = 12 V ÷ 1790 Ω ≈ 6.704 mA

Step 3 — per-resistor voltage drops

Resistor	Vᵢ = I × Rᵢ	Pᵢ = I² × Rᵢ
R1 = 100 Ω	0.670 V	4.49 mW
R2 = 220 Ω	1.475 V	9.89 mW
R3 = 470 Ω	3.151 V	21.12 mW
R4 = 1 000 Ω	6.704 V	44.94 mW
Total	12.000 V	80.44 mW

KVL check: 0.670 + 1.475 + 3.151 + 6.704 = 12 V ✓

The 1 kΩ resistor drops more than half the supply and dissipates the most power. All four are well within a standard ¼ W (250 mW) rating, giving a comfortable safety margin.

Formula note

The formula Pᵢ = I² × Rᵢ follows from substituting Ohm’s law (V = IR) into the power equation P = V × I. An equivalent form is Pᵢ = Vᵢ² / Rᵢ; both give identical answers. The total power delivered by the source equals P_total = V × I = I² × Rₜ, which also equals the sum of all individual resistor powers — energy is conserved.

When choosing physical resistors, always ensure the rated wattage exceeds the calculated dissipation by at least 50 %. For example, if a resistor dissipates 150 mW, select a ½ W (500 mW) component rather than the bare-minimum ¼ W to avoid thermal stress and premature failure.