Internal Resistance Calculator

About the Internal Resistance Calculator

Every real voltage source — batteries, generators, solar cells — has internal resistance that causes the terminal voltage to drop under load. Understanding this internal resistance is crucial for predicting battery performance, sizing power systems, and diagnosing aging or damaged cells.

The internal resistance is measured by comparing the open-circuit voltage (EMF) with the terminal voltage under a known load current: r = (EMF − V_load) / I. This simple measurement reveals how much power is wasted as heat inside the source and how the terminal voltage will sag under increasing load.

This calculator computes internal resistance, voltage drop, power loss, efficiency, short-circuit current, and maximum power transfer conditions. It includes a voltage-vs-current table showing how the terminal voltage decreases as load increases, plus reference data for common battery types. Battery technicians, electronics designers, and physics students can use it to compare sources and predict behavior under load.

When This Page Helps

Internal resistance is not printed on battery labels but profoundly affects performance. A source with high internal resistance cannot deliver high currents cleanly and wastes more energy as heat. This calculator determines internal resistance from measurable quantities and predicts behavior across load conditions, helping you choose batteries, diagnose degradation, and design efficient circuits.

How to Use the Inputs

1. Measure and enter the open-circuit voltage (EMF) with no load connected.
2. Measure and enter the terminal voltage under a known load.
3. Enter the load current being drawn during the loaded measurement.
4. Optionally enter the number of cells in series for battery pack calculations.
5. Read the internal resistance, voltage drop, power loss, and efficiency.
6. Review the voltage vs load current table to predict behavior at different loads.
7. Compare against the typical internal resistance reference table.

Example Calculation

Tips & Best Practices

• Internal resistance increases as batteries age or discharge — it is the best indicator of battery health.
• Measure open-circuit voltage after the battery has rested for at least 30 minutes for accurate EMF.
• For maximum power transfer, match the load resistance to internal resistance — but this is only 50% efficient.
• High-drain applications (power tools, EV motors) demand batteries with very low internal resistance.
• Temperature affects internal resistance: cold batteries have higher resistance, reducing their current capacity.
• For cells in series, total internal resistance is the sum of individual cell resistances.

Battery Health and Aging

Internal resistance is the most reliable indicator of battery health. New lithium-ion cells have internal resistance of 20-50 mΩ, which gradually increases over hundreds of charge cycles. When resistance doubles from its initial value, the battery is typically considered end-of-life for demanding applications. Battery management systems (BMS) monitor internal resistance trends to predict remaining useful life.

Maximum Power Transfer Theorem

The maximum power transfer theorem states that maximum power is delivered to a load when its resistance equals the source internal resistance. While this maximizes output power (P_max = EMF²/4r), it is only 50% efficient. In practice, most systems operate with R_load >> r for high efficiency. The exception is RF and audio circuits where impedance matching is critical for signal quality.

Multi-Cell Battery Packs

In series-connected battery packs, the total internal resistance is the sum of all cell resistances. If one cell has abnormally high resistance, it limits the pack's current capability and may overheat under load. This is why battery pack manufacturers carefully match cells by internal resistance (cell balancing) and why BMS systems monitor individual cell voltages.

Frequently Asked Questions

• What is internal resistance?

  Internal resistance is the inherent resistance inside a voltage source (battery, generator, solar cell) that causes the terminal voltage to drop when current flows. It is caused by electrode and electrolyte resistance in batteries, or winding resistance in generators.

• How do I measure internal resistance?

  Measure the open-circuit voltage (no load), then measure the voltage under a known load current. Internal resistance = (V_oc − V_loaded) / I_loaded. Dedicated battery testers use AC impedance methods for closer estimates.

• What is a good internal resistance for a car battery?

  A healthy car battery typically has 5-15 mΩ internal resistance. Values above 20-30 mΩ indicate aging. Above 50 mΩ, the battery may struggle to start the engine, especially in cold weather.

• What is maximum power transfer?

  Maximum power is delivered to the load when R_load = r_internal. However, this condition is only 50% efficient — half the power is wasted inside the source. Power systems aim for R_load >> r for high efficiency.

• Does internal resistance change with state of charge?

  Yes. Internal resistance is lowest at full charge and increases as the battery discharges. Near the end of discharge, resistance rises sharply, causing voltage to collapse under load.

• What is the short-circuit current?

  I_sc = EMF / r. For a car battery (12.6V, 10 mΩ), this could be 1,260A — enough to melt wires and cause fires. This is why fuses and circuit breakers are essential. Never short-circuit a battery.