Battery Runtime Calculator

Technical article

Understand Battery Runtime Calculator

This calculator finds the theoretical runtime t of a battery under a constant load from voltage U, capacity Q, efficiency η and load power P — or solves for any one of these given the other three. It explains why actual runtime is usually below the simple ratio of nominal energy to power.

What does this quantity describe?

Theoretical runtime follows from the battery's usable energy (U·Q·η) divided by the constant load power P: t = U·Q·η/P. Efficiency η bundles losses from the discharge curve, internal resistance and any downstream converter.

Much like a fuel tank, a battery runs out sooner under higher power draw: doubling load power P at the same capacity roughly halves runtime — provided efficiency stays constant throughout the discharge.

Formula and variables

t = U · Q · η / P

t = U · Q · η / P
P = U · Q · η / t
Q = P · t / (U · η)

Symbol / input	Meaning
Runtime t	Theoretical supply duration at constant load.
Average battery voltage U	Average voltage during discharge.
Capacity Q	Rated capacity; usable fraction is represented by efficiency.
Load power P	Electrical input power including continuous auxiliaries.
Overall efficiency η	Share of nominal energy usable after converter and discharge losses.

Choose the inputs correctly

Enter the three known quantities to find the fourth. Efficiency η ranges between 0 and 1 (or 0-100%) and bundles all losses between nominal energy and the energy actually usable at the load.

How to use the calculator

Select the target quantity and enter the three known values with units. Without more precise manufacturer data, an efficiency of about 0.8-0.9 for battery plus converter is a reasonable first estimate.

Worked example

Given U = 48 V, Q = 50 Ah, P = 480 W and η = 0.85, substitution gives t = 48 V · 50 Ah · 0.85 / 480 W ≈ 4.25 h.

Understand the result and units

A calculated runtime of 4.25 hours is an approximation under constant load. In practice, actual runtime can differ if load fluctuates, battery temperature is outside the rated range, or the manufacturer specifies a C-rate-dependent capacity reduction.

Runtime is given in hours (h), capacity in amp-hours (Ah), power in watts (W) and voltage in volts (V). Efficiency η is dimensionless.

Typical applications

Runtime estimates are used to size backup power supplies, mobile devices, e-bikes and small electric vehicles, and to dimension battery storage for a defined bridging time.

Assumptions, limits and common mistakes

The formula assumes constant power, a discharge-averaged voltage, and constant efficiency. Real batteries deliver less usable capacity at high discharge currents (high C-rate) than the simple calculation implies — an effect manufacturer datasheets often show as a capacity-vs-C-rate curve.

Common mistake: Do not neglect efficiency: without η, runtime is systematically overestimated. Also, do not assume nominal capacity stays constant regardless of actual discharge current, since high currents can reduce a real cell's usable capacity.

Frequently asked questions

What efficiency should I assume if the manufacturer doesn't state one?

For battery plus a downstream converter, 0.8-0.9 is a common first estimate; for precise sizing, use the actual datasheet.

Why is real runtime often shorter than calculated?

High discharge currents, low temperatures and cell ageing reduce usable capacity below the nominal rating, an effect this simple formula does not capture.

How does runtime change at double the load power?

All else equal, runtime roughly halves, since t is inversely proportional to P.