Internal Resistance Calculator
Enter any three of EMF, load resistance, current, and terminal voltage to solve for the fourth. The calculator also shows power dissipated inside the source, circuit efficiency, and the voltage drop across the internal resistance. Choose which quantity to solve for, and the step panel walks through every formula with your actual numbers.
Formula
Worked example
A 12 V car battery delivers 1 A through a 10 ohm load. Using r = emf/I - R: r = 12/1 - 10 = 2 ohm. Terminal voltage: V = 12 - 1 x 2 = 10 V. Internal power loss: P = 1^2 x 2 = 2 W. Load power: 1^2 x 10 = 10 W. Efficiency: 10 / (10 + 2) = 83.3%.
What is internal resistance?
Every real battery, generator, or power supply has some resistance inside it. This is called internal resistance (symbol r) and it arises from the electrolyte, electrode materials, and connections within the cell. When current flows, some of the electromotive force (EMF) is dropped across this internal resistance, so the voltage available at the terminals is always less than the open-circuit EMF. A fresh, high-quality battery has very low internal resistance, while an aged or heavily discharged battery has higher internal resistance that causes noticeable voltage sag under load.
The core equations
The fundamental relationship is emf = I (R + r), where emf is the open-circuit voltage in volts, I is the current in amperes, R is the external load resistance in ohms, and r is the internal resistance in ohms. Rearranging gives the internal resistance formula r = emf/I - R, the terminal voltage formula V = emf - Ir, and the current formula I = emf / (R + r). Power dissipated internally is P_int = I squared times r, which grows quadratically with current, this is why high-drain devices heat up batteries quickly. Circuit efficiency is eta = R / (R + r), the fraction of total power that reaches the external load.
How to measure internal resistance
The simplest method uses two load tests. Connect a known load resistance R1 and measure terminal voltage V1 and current I1. Then switch to a different known load R2 and measure V2 and I2. Internal resistance is r = (V1 - V2) / (I2 - I1). You can also measure the open-circuit voltage (emf) with a high-impedance voltmeter, then connect a known load and measure the new terminal voltage V under current I. From those two readings r = (emf - V) / I. Purpose-built battery testers inject a small AC signal at a known frequency and measure the impedance response, giving the most accurate results.
Internal resistance in practice
Internal resistance matters most in high-current applications. A car starter motor can draw 200 A or more; even a 0.01 ohm battery with that current drops 2 V internally. In consumer electronics, a worn battery may show nearly full voltage with no load but sag to below the cutoff voltage the moment the device draws current. Lithium-ion cells used in electric vehicles are engineered for extremely low internal resistance (sometimes below 1 milliohm per cell) so that packs can deliver tens of kilowatts efficiently. In audio and RF circuits, source resistance affects noise and bandwidth, so impedance matching is designed around the source r.
Typical internal resistance by battery type
| Battery Type | Typical r (ohm) | Notes |
|---|---|---|
| Alkaline AA (fresh) | 0.1 to 0.3 | Rises to 1+ ohm near end of life |
| Alkaline AA (depleted) | 1.0 to 2.0 | High r causes voltage sag under load |
| Alkaline 9V (fresh) | 1.0 to 2.0 | Nine 1.5V cells stacked in series |
| Li-ion 18650 (fresh) | 0.02 to 0.08 | Very low r, high power density |
| Li-ion 18650 (aged) | 0.15 to 0.5 | r increases with cycle count |
| Lead-acid car battery (good) | 0.005 to 0.02 | Low r enables high cold-cranking amps |
| Lead-acid car battery (old) | 0.1 to 0.5 | Sulfation raises r significantly |
| NiMH AA (fresh) | 0.05 to 0.15 | Good balance of r and capacity |
| Supercapacitor | 0.001 to 0.01 | Extremely low r, but low energy density |
| Ideal voltage source | 0 | Theoretical: terminal voltage never drops |
Representative values at room temperature and moderate state of charge. Actual values vary with age, temperature, and discharge rate.
Frequently asked questions
What causes internal resistance in a battery?
Internal resistance comes from several physical sources inside the cell. The electrolyte has finite ionic conductivity, so ions moving between electrodes experience resistance. The electrode materials themselves have electronic resistance. The separator between electrodes adds resistance. Contact resistances at current collectors and terminals contribute too. As a battery ages, chemical changes such as electrolyte decomposition, electrode cracking, and the buildup of resistive films on electrode surfaces all increase the internal resistance.
Why does terminal voltage drop under load?
When current flows through the battery, Ohm's law demands a voltage drop of I times r across the internal resistance. This voltage is unavailable at the terminals. The more current is drawn, the larger the drop. At the extreme short-circuit condition (R = 0), the entire EMF is dropped internally and the terminal voltage falls to zero. This is why you should never short-circuit a battery.
What is a good value for internal resistance?
It depends entirely on the application. A fresh AA alkaline cell typically has 0.1 to 0.3 ohm. A quality 18650 lithium-ion cell has 0.02 to 0.08 ohm. A lead-acid car battery might be 0.005 to 0.02 ohm. For high-power applications the lower the better, but even 1 ohm is acceptable for a low-drain device. As a rule of thumb, once the internal resistance exceeds roughly 20% of the load resistance, efficiency and terminal voltage sag become significant.
How does temperature affect internal resistance?
Cold temperatures increase internal resistance significantly. At 0 degrees C, an alkaline battery may have double the internal resistance it has at 25 degrees C, which is why torch batteries fail in winter. Lithium-ion cells are less affected but still show higher internal resistance below freezing. At very high temperatures, internal resistance usually drops, but other degradation mechanisms accelerate, shortening battery life.
Can I connect batteries in parallel to reduce internal resistance?
Yes. When n identical batteries are connected in parallel, the combined internal resistance is r/n, just like parallel resistors. Two cells with 0.1 ohm each give a combined r of 0.05 ohm. The combined capacity also doubles. However, batteries in parallel should be matched in voltage and state of charge to avoid large circulating currents between them.
What is the maximum power transfer theorem and how does internal resistance relate?
Maximum power is delivered to the load when the load resistance equals the source internal resistance (R = r). At that point, efficiency is exactly 50% since equal power is dissipated internally and in the load. For power delivery you want R much greater than r to keep efficiency high. For maximum power transfer (important in signal circuits and antennas) you match R to r. These two goals are in opposition, so the right choice depends on whether you need efficiency or maximum power.