Internal Resistance Calculator (battery r from open-circuit and loaded voltage)

Understanding the internal resistance calculator — concept and principle

This calculator finds the internal resistance of a battery or power supply from its open-circuit voltage and its terminal voltage under a known load current or load resistance. It also gives the short-circuit current, power wasted inside, efficiency and the maximum power the source can deliver. It is useful for testing car batteries, lithium cells and bench supplies.

The 0.5 V the battery loses under load is the current flowing through its own resistance.

How it is calculated

V = ε − I r, so r = (ε − V) ÷ I

If the load resistance R is known: I = V ÷ R and r = R (ε ÷ V − 1)

Short-circuit current = ε ÷ r; loss inside = I² r; power to load = V I

Efficiency = V ÷ ε; maximum power = ε² ÷ (4r), into a load equal to r

ε is the open-circuit voltage (EMF) in volts; r is shown in mΩ and Ω.

The principle

A real source behaves like an ideal voltage source in series with a small resistor. With no current flowing, the terminal voltage equals the EMF. When current flows, part of the EMF is dropped across the internal resistance, so the terminal voltage sags in proportion to the current. Measuring how much it sags at a known current reveals r. Maximum power is delivered when the load equals r, but then half the energy is wasted inside, so practical loads are much larger than r.

Worked example

Default inputs: load current mode, ε = 12.6 V, V = 12.1 V, I = 20 A.

r = (12.6 − 12.1) ÷ 20 = 0.025 Ω = 25 mΩ.
Short-circuit current = 12.6 ÷ 0.025 = 504 A.
Power lost inside = 20² × 0.025 = 10 W; power to the load = 12.1 × 20 = 242 W.
Efficiency = 12.1 ÷ 12.6 = 96.03%.
Maximum power to a matched load = 12.6² ÷ (4 × 0.025) = 1,588 W.

Each point is the calculator re-run with only “Load current (A)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Load current (A)	Internal resistance (mΩ)
5	100
10	50
15	33.33
20	25
25	20
30	16.67
40	12.5

How to read the result

Internal resistance rises as batteries age, get cold or discharge, so a rising r is a sign of wear. A healthy car battery has a low resistance that lets it deliver hundreds of amperes for starting. Compare results only at similar temperature and state of charge.

Common mistakes

Measuring the open-circuit voltage right after charging, when it is temporarily high.
Taking the loaded reading too slowly, while the voltage keeps sagging.
Ignoring the resistance of leads and clamps, which adds to r.

Keep in mind: Short-circuit currents can be very large. Never short a battery to test it; use a controlled load and protective equipment.

Frequently asked questions

Why does a battery voltage drop under load?

Current flowing through the internal resistance causes a voltage drop inside the battery.

Is maximum power the best operating point?

No. At maximum power, efficiency is only 50%.

Does internal resistance change with temperature?

Yes. For most batteries it rises noticeably in the cold.

Sources: Standard circuit results: terminal voltage V = ε − Ir and the maximum power transfer theorem

Checked 9 Nov 2026. Terminal voltage of a source with internal resistance V = ε − Ir and the maximum-power-transfer theorem (load equal to r) — standard circuit results.

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