Thermal Energy Calculator
The total energy to take a substance from one temperature to another — including any melting or boiling the range crosses.
Ice to steam, all in one calculation.
How the thermal energy calculator works
Heating through a phase change is not one calculation but several: sensible heat (mcΔT) in each phase, plus latent heat (mL) at each transition the range actually crosses, added in sequence. A range that stops exactly at 0 °C or 100 °C does not include that phase change — heating water from 0 to 100 is sensible heat only.
For water from −20 °C to 120 °C that is five stages, and the two latent terms dominate: heating the water across its whole liquid range costs less than half of what boiling it costs.
Formula: Q = Σ m cᵢ ΔTᵢ + Σ m Lᵢ
Worked examples
| Inputs | Total energy | Note |
|---|---|---|
| Ice at −20 °C to steam at 120 °C | 3,094,660 J | 3.1 MJ, 83% of it latent |
| Just heating water 0→100 °C | 418,600 J | 419 kJ, no phase change |
| Ice at −10 °C to water at 10 °C | 396,790 J | melting dominates the 20-degree span |
FAQFrequently asked questions
Why is so much of the energy latent?
Because boiling water costs 2,260 kJ/kg against the 419 kJ/kg needed to heat it across its entire liquid range. The phase change dominates.
What are the specific heats used?
Ice 2,093 J/kg·K, water 4,186, steam 2,010 — and latent heats of 334 kJ/kg for fusion and 2,260 for vaporization.
Does pressure change this?
Yes. These are the values at one atmosphere. At altitude water boils lower and its latent heat rises slightly.
Why does the temperature stall while ice melts?
Because every joule goes into breaking the crystal lattice. Nothing is left to raize the temperature until the last ice has gone.
Can I run it in reverse for cooling?
The energies are the same in magnitude — freezing releases exactly what melting absorbs. This page computes the heating direction.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Institute of Standards and Technology — the US measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.