Electromotive Force (EMF) Calculator
Find the electromotive force (EMF) of a battery or cell. Enter the terminal voltage under load, the current drawn and the internal resistance to compute EMF, internal voltage drop, power lost and source efficiency.
V
A
Ω
Total energy per unit charge supplied by the source (open-circuit voltage)
- 1
Internal voltage drop I × r
5 A × 0.04 Ω = 0.2Voltage lost inside the source due to its internal resistance. - 2
EMF = V_terminal + I × r
11.8 V + 0.2 V = 12
How does this calculator work?
EMF = terminal voltage + internal voltage drop: ε = V_t + I × r. A 12 V lead-acid battery (r = 0.04 Ω) delivering 50 A has EMF = 12 + 50 × 0.04 = 14 V; internal power loss = 50² × 0.04 = 100 W; efficiency = 12/14 ≈ 86%.
Formula
How this is calculated
Electromotive force (EMF, symbol ε) is the energy per unit charge that a source — a battery, cell or generator — supplies to the circuit. It is measured in volts and represents the open-circuit voltage: the voltage you would measure with a perfect voltmeter drawing no current. Every real source has internal resistance r (from electrode materials, electrolyte and connections), which causes a voltage drop I × r whenever current I flows. The terminal voltage V_t available at the battery's poles is always lower than the EMF under load: ε = V_t + I × r, or equivalently V_t = ε − I × r.
Measuring EMF in practice: connect the battery to a known load resistor and measure terminal voltage V_t and current I simultaneously. Then ε = V_t + I × r. If you also know the open-circuit voltage (measured with negligible current draw), internal resistance follows from r = (ε − V_t) / I. Internal resistance for a fresh alkaline AA cell is about 0.15–0.3 Ω; a 12 V lead-acid car battery is 0.01–0.05 Ω; a lithium-ion cell is 0.05–0.2 Ω, rising sharply as the cell ages or temperature falls.
The power dissipated inside the source as heat is P_loss = I² × r, which reduces the energy delivered to the external circuit. Source efficiency η = V_t / ε × 100% shows what fraction of the source energy reaches the load. At high discharge rates the sag in terminal voltage and the rise in internal heat loss both become severe — which is why battery capacity ratings are always quoted at a specified discharge rate.
Frequently asked questions
EMF is the total energy per coulomb a source can supply — its open-circuit voltage. Terminal voltage is what appears at the output terminals when current flows. The difference is the internal voltage drop I × r: a larger current draws a bigger drop, leaving less for the external circuit. An ageing battery has higher internal resistance, so terminal voltage sags more under the same load.
Connect the battery to a known load. Measure the open-circuit voltage V_oc (≈ EMF) with negligible current, and the loaded terminal voltage V_t under a measured current I. Internal resistance r = (V_oc − V_t) / I. Alternatively, measure V_t with two different load currents I₁ and I₂: r = (V₁ − V₂) / (I₂ − I₁).
A larger current causes a larger internal drop I × r, leaving less voltage for the external circuit. Internal power loss I² × r also heats the cell, which can further increase resistance. A discharged battery may still measure close to its nominal voltage open-circuit but collapse to near zero under load, because its internal resistance has risen to the point where I × r ≈ EMF.
TG we-Calculate Editorial Team. (2026). Electromotive Force (EMF) Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/electromotive-force-calculator
TG we-Calculate Editorial Team. "Electromotive Force (EMF) Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/electromotive-force-calculator.
TG we-Calculate Editorial Team, "Electromotive Force (EMF) Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/electromotive-force-calculator
@misc{wecalculate_electromotive_force_calculator, title = {Electromotive Force (EMF) Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/electromotive-force-calculator}}, year = {2026}, note = {TG we-Calculate} }
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