Battery Internal Resistance

Rint = (Voc − Vload) / I

Quick answer

This calculator solves R_int = (V_oc − V_load) / I for Internal Resistance. With Open-Circuit Voltage 120 V, Loaded Voltage 56.4 V, Load Current 20 A, the result is 3.18 Ω. It solves in 4 directions, so you can enter the values you have and get the one you need.

Calculator

Internal Resistance (mΩ)
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Formula

R_int = (V_oc − V_load) / I

Description

Battery internal resistance causes a voltage drop proportional to discharge current, reducing the terminal voltage under load. It can be measured by comparing the open-circuit voltage (no load) to the voltage under a known load current. Internal resistance increases as the battery ages, as temperature decreases, and as the state of charge decreases. It is a key indicator of battery health (state of health, SoH) and determines the maximum current the battery can deliver before the terminal voltage drops below the minimum operating voltage.

Variables

  • R_int — Internal resistance (Ω)
  • V_oc — Open-circuit voltage, no load (V)
  • V_load — Terminal voltage under load (V)
  • I — Load current (A)

Practical Notes

Typical internal resistances: 18650 Li-ion 20-80 mΩ (new), lead-acid car battery 5-10 mΩ, coin cell CR2032 10-30 Ω. A new 18650 cell at 50 mΩ drawing 3 A drops 150 mV. When internal resistance doubles from its initial value, the battery is generally considered end-of-life. AC impedance measurement (EIS) at 1 kHz provides a more accurate and faster measurement than DC methods.

Symbols and units

Symbol Meaning Default unit Accepted units
Rint Internal Resistance mΩ mΩ, Ω, kΩ, MΩ
Voc Open-Circuit Voltage V pV, nV, µV, mV, V, kV
Vload Loaded Voltage V pV, nV, µV, mV, V, kV
I Load Current A pA, nA, µA, mA, A, kA

Step by step

  1. 1. What you know: Open-Circuit Voltage 120 V, Loaded Voltage 56.4 V, Load Current 20 A
  2. 2. The relation: R_int = (V_oc − V_load) / I
  3. 3. Substitute: Voc = 120 V, Vload = 56.4 V, I = 20 A
  4. 4. Result: Internal Resistance = 3.18 Ω

Related quantities from the same inputs

  • P = V × I = 2.4 kW

Nearest standard component values

Series Nearest value Error
E12 3.3 Ω 3.8%
E24 3.3 Ω 3.8%

Worked examples

Minimum range

Given: Open-Circuit Voltage 3.3 V, Loaded Voltage 1.55 V, Load Current 20 mA

Result: Internal Resistance = 87.5 Ω

Low range

Given: Open-Circuit Voltage 33 V, Loaded Voltage 15.5 V, Load Current 0.2 A

Result: Internal Resistance = 87.5 Ω

Typical

Given: Open-Circuit Voltage 120 V, Loaded Voltage 56.4 V, Load Current 20 A

Result: Internal Resistance = 3.18 Ω

High range

Given: Open-Circuit Voltage 2.3 kV, Loaded Voltage 1.08 kV, Load Current 1 kA

Result: Internal Resistance = 1.22 Ω

Maximum range

Given: Open-Circuit Voltage 23 kV, Loaded Voltage 10.8 kV, Load Current 10 kA

Result: Internal Resistance = 1.22 Ω

Solving for each variable

Solve for Internal Resistance

Open-Circuit Voltage 3.3 V, Loaded Voltage 1.55 V, Load Current 20 mA → 87.5 Ω

Solve for Open-Circuit Voltage

Internal Resistance 0.1 mΩ, Loaded Voltage 0.726 V, Load Current 2 mA → 0.726 V

Solve for Loaded Voltage

Internal Resistance 0.1 mΩ, Open-Circuit Voltage 0.33 V, Load Current 2 mA → 0.33 V

Solve for Load Current

Internal Resistance 0.1 mΩ, Open-Circuit Voltage 0.33 V, Loaded Voltage 0.726 V → -3.96 kA

How Internal Resistance changes with Open-Circuit Voltage

Open-Circuit Voltage (input) Internal Resistance (result)
60 V 0.18 Ω
90 V 1.68 Ω
120 V 3.18 Ω
0.18 kV 6.18 Ω
0.24 kV 9.18 Ω
0.48 kV 21.18 Ω
0.84 kV 39.18 Ω
1.2 kV 57.18 Ω

The same result in other units

Unit Value
mΩ 3180
Ω 3.18
kΩ 0.00318

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Frequently asked questions

How do you calculate Battery Internal Resistance?

Use R_int = (V_oc − V_load) / I. With Open-Circuit Voltage 120 V, Loaded Voltage 56.4 V, Load Current 20 A, Internal Resistance works out to 3.18 Ω.

What is the formula for Battery Internal Resistance?

The formula is R_int = (V_oc − V_load) / I. Battery internal resistance causes a voltage drop proportional to discharge current, reducing the terminal voltage under load.

How do you find Open-Circuit Voltage when you know the other values?

Rearrange for Open-Circuit Voltage: with Internal Resistance 0.1 mΩ, Loaded Voltage 0.726 V, Load Current 2 mA, Open-Circuit Voltage is 0.726 V.

How do you find Loaded Voltage when you know the other values?

Rearrange for Loaded Voltage: with Internal Resistance 0.1 mΩ, Open-Circuit Voltage 0.33 V, Load Current 2 mA, Loaded Voltage is 0.33 V.

What units does Battery Internal Resistance use?

Internal Resistance is shown in mΩ, Ω, kΩ. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

Related Concepts

All Battery formulas →
Battery Runtime Battery Energy Battery Loaded Voltage Battery Charge Time Battery Self-Discharge Battery Temperature Derating Cell Balancing Current Battery Internal Resistance

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