Latent Heat Calculator
Latent heat is the energy a substance absorbs or releases as it changes phase, melting, freezing, boiling, condensing or subliming, without any change in temperature. Choose what to solve for (the heat Q, the mass m, or the specific latent heat L), pick a substance preset or enter your own, and this calculator works the relation Q = m·L both ways. It reports the energy in joules, kilojoules, kilocalories and kilowatt-hours, and can price that energy at an electricity rate.
Formula
Worked example
Melt 0.5 kg of ice at 0°C. The specific latent heat of fusion of water is L = 334,000 J/kg, so Q = 0.5 × 334,000 = 167,000 J = 167 kJ ≈ 39.9 kcal. The water stays at 0°C the entire time, the energy goes purely into the phase change. Working backward, 167,000 J ÷ 334,000 J/kg returns the original 0.5 kg.
What latent heat means
When you heat a block of ice it warms steadily until it reaches 0°C, and then something strange happens: you keep adding energy but the temperature stops climbing while the ice turns to water. That hidden, or "latent," energy is the latent heat. It is the energy required to break (or, in reverse, to reform) the bonds that hold a substance in a particular phase, and it is exchanged at a constant temperature throughout the melting, freezing, boiling, condensing or subliming process. Because the thermometer does not move, the energy is invisible to the eye, yet it can be enormous, far larger than the energy needed to change the temperature of the same mass by several degrees.
The formula Q = m·L and how to rearrange it
The total latent heat is the product of two things: the mass m of substance changing phase and the specific latent heat L of that particular transition. Specific latent heat is a material property measured in joules per kilogram, and it differs for each kind of phase change. The latent heat of fusion (Lf) applies to melting and freezing, the latent heat of vaporization (Lv) applies to boiling and condensing, and the latent heat of sublimation (Ls) applies to a solid turning straight into gas, like dry ice. For almost every substance Lv is much larger than Lf because pulling molecules completely apart into a gas costs more energy than merely loosening them into a liquid. This calculator solves the relation in all three directions: Q = m·L when you know mass and L, m = Q / L when you know the energy and L, and L = Q / m when you have measured both the energy and the mass and want the material property itself.
Solving for mass or specific latent heat
Choosing what to solve for turns the tool into three calculators in one. Leave the "Solve for" menu on heat energy to get Q from a mass and a substance, the most common case. Switch it to mass to find how much ice a given amount of energy can melt, or how much water a boiler can evaporate, by dividing the energy by L. Switch it to specific latent heat to run the experiment in reverse: supply a known amount of energy to a known mass, measure nothing but those two numbers, and the calculator returns L, which you can compare against the reference table to identify the substance. Mass can be entered in kilograms, grams, pounds or ounces, and every input is converted internally so the math stays in SI units.
Energy units, cost, and everyday relevance
The result is reported in joules, kilojoules, kilocalories and kilowatt-hours so it slots into whatever context you are working in, a physics homework set, a kitchen, or an energy bill. Turn on the cost estimate and enter your electricity rate to see what that energy would cost to supply, a planning figure that ignores the inefficiency of any real heater. Latent heat explains why a pot of boiling water stays at 100°C no matter how high you turn the burner, why sweating cools your skin as perspiration evaporates, and why steam at 100°C causes far worse burns than liquid water at the same temperature, the condensing steam dumps its entire latent heat of vaporization into your skin. Refrigerators, heat pumps and air conditioners exploit the same principle, absorbing latent heat as a refrigerant evaporates and releasing it as it condenses elsewhere. This calculator handles only the phase change itself; to model heating a substance up to its melting or boiling point and then changing its phase, combine this result with the sensible heat Q = m·c·ΔT for each temperature segment.
Specific latent heat of common substances
| Substance | Latent heat of fusion [kJ/kg] | Latent heat of vaporization [kJ/kg] |
|---|---|---|
| Water | 334 | 2256 |
| Ethanol | 108 | 855 |
| Ammonia | 332 | 1370 |
| Carbon dioxide | sublimes (571) | n/a |
| Nitrogen | 25.7 | 199 |
| Oxygen | 13.9 | 213 |
| Mercury | 11.4 | 294 |
| Lead | 23.0 | 871 |
| Aluminum | 397 | 10500 |
| Iron | 247 | 6090 |
| Gold | 64.5 | 1645 |
Approximate specific latent heats of fusion (melting) and vaporization (boiling) in kJ/kg, at standard pressure. Carbon dioxide sublimes rather than melting at 1 atm. Values vary slightly with source.
Frequently asked questions
How do I find the mass from a known amount of latent heat?
Rearrange Q = m·L to m = Q / L: divide the heat energy by the specific latent heat of the transition. For example, 668,000 J applied to ice (Lf = 334,000 J/kg) melts 668,000 ÷ 334,000 = 2 kg. Set the "Solve for" menu to mass and the calculator does this for you.
How do I calculate the specific latent heat of a substance?
Use L = Q / m: divide the total energy supplied during the phase change by the mass that changed phase. Measuring the energy delivered to a known mass of melting or boiling material and dividing gives L, which you can match against a table to identify the substance. Choose "specific latent heat" in the "Solve for" menu.
What is the difference between latent heat and specific heat?
Specific heat (Q = m·c·ΔT) is the energy to change a substance’s temperature while it stays in one phase. Latent heat (Q = m·L) is the energy to change its phase at a constant temperature. A full heating problem often uses both: specific heat for each temperature ramp and latent heat for each melting or boiling step.
Why is the latent heat of vaporization larger than fusion?
Melting only loosens the rigid structure of a solid into a flowing liquid, so molecules stay close together. Vaporizing must pull the molecules completely apart into a gas, overcoming nearly all of the intermolecular attraction. That takes much more energy: for water, 2256 kJ/kg to boil versus only 334 kJ/kg to melt.
Does the temperature change during latent heat transfer?
No. The defining feature of latent heat is that temperature stays constant throughout the phase change. All the energy goes into breaking or forming bonds rather than speeding up molecules, so ΔT is zero. The temperature only resumes changing once the substance is fully melted, frozen, boiled, condensed or sublimed.