Battery Heat Dissipation Calculator (Bernardi Equation)
Estimate the heat a battery cell generates during charge or discharge, and the heat a cooling system must remove from a pack. The calculation uses the Bernardi equation as given in Frontiers in Energy Research 14:1817181 (2026), Equation 3, after Bernardi, Pawlikowski and Newman, J. Electrochem. Soc. 132, 5-12 (1985): irreversible Joule heat plus reversible entropic heat.
Q = I² · R − I · T · dU/dT
I: signed current in A (positive in discharge, negative in charge) · R: internal resistance in Ω · T: cell temperature in K · dU/dT: entropic coefficient in V/K · Q: cell heat in W
Pack heat = n · Q · Heat energy E = n · Q · t (J), and E in Wh = J ÷ 3600
Calculator
Results
Negative means net heat absorption (cooling) by the reaction.
Formulas with your numbers
How to use the calculator
- Choose the direction: Discharge or Charge. The current is taken as positive in discharge and negative in charge.
- Enter the current magnitude |I| in A, or switch the current input to C-rate and enter the C-rate together with the cell capacity in Ah.
- Enter the internal resistance R in mΩ or Ω, measured at the cell temperature.
- Enter the cell temperature T in °C or K.
- Enter the entropic coefficient dU/dT in mV/K, with its sign.
- Enter the number of cells n that carry the same current. Add a duration t in s, min or h if you also need the heat energy.
- Press Calculate. Read the signed current, the Joule heat, the reversible heat, the cell heat, the pack heat and, with a duration, the heat energy in J and Wh, followed by every formula with your numbers.
Notes on the two heat terms
- The first term, I² · R, is irreversible Joule (ohmic) heating and grows with the square of the current.
- The second term, −I · T · dU/dT, is reversible entropic heat from lithium intercalation, with I above 0 in discharge as in the Bernardi convention.
- For NCM cathodes the entropic coefficient typically ranges from −0.2 to +0.4 mV/K across the state of charge (Frontiers 2026).
- Internal resistance rises at low temperature, so use R measured at the cell temperature.
Disclaimer
This calculator gives an estimate for thermal design. It is not a substitute for cell supplier data or calorimetry.