Latent Heat Calculator

At a phase change, heat flows and the thermometer refuses to move — the energy goes into rearranging molecules, not warming them. Enter the mass and the material’s latent heat, and this calculator returns the energy of melting, freezing, boiling or condensing it.

Heat Without Temperature: Black's Hidden Quantity

Joseph Black's second great surprise (the heat-capacity page holds the first): ice at 0 °C absorbs a large, definite quantity of heat while staying at 0 °C, becoming water at 0 °C — the energy spent breaking the crystal's bonds rather than raising kinetic energy. He named it latent (hidden) heat; the equation is his bookkeeping, Q = mL, with a different L for each transition: fusion (melting) and vaporisation the giants, vaporisation's typically five to seven times fusion's for the same substance, since escaping a liquid entirely costs more than loosening a solid. The thermometer's flat line during a phase change is not the energy stopping — it is the energy changing jobs — and every technology that stores or moves heat cheaply, from ice houses to heat pumps to the phase-change packs in a laptop's cooling pad, is an exploitation of the plateau this page prices.

Worked Example: A Kilogram of Ice

The defaults melt a kilogram of ice at 0 °C: Q = 1 × 334,000 = 334,000 J (334 kJ, 0.0928 kWh). For scale, that is the heat the capacity page charges for raising the resulting litre of water by almost 80 degrees — delivered here without the temperature moving at all. Now the reverse column's champion: vaporising a kilogram of water costs 2,260,000 J, 6.8 times the melt — which is why steam is such a potent heat courier (condensing in a radiator, it dumps its 2.26 MJ per kilogram at a constant 100 °C) and why a steam scald is so much worse than a hot-water one: the condensing gram on skin releases its latent hoard plus its cooling warmth, the double invoice the widget's note refers to.

The Atmosphere's Engine

Scale the worked example by an ocean: every kilogram of seawater that evaporates carries 2.26 MJ of latent heat aloft invisibly in the vapour, released again where the vapour condenses — into cloud, rain, and the dynamics of storms. A hurricane is, in energetic terms, a latent-heat engine of continental appetite, condensing vapour at rates that liberate the equivalent of a large power station's output per raindrop census; monsoons, the water cycle's whole circulation, and the moderation of tropical sea temperatures all keep their accounts in L. The calculator's humble multiplication — mass times a constant — is, at planetary scale, the largest single energy transport in the climate system, and it runs silently because the heat is hidden in exactly Black's sense: present, enormous, and invisible to thermometers.

The Ice House Economy

Before refrigeration, civilisation ran a global trade in this equation: New England ponds were harvested in winter, the ice shipped as far as Calcutta and Sydney packed in sawdust, each block a banked 334 kJ per kilogram of cold, drawn down cube by cube in the iceboxes of the tropics. Frederic Tudor, the "Ice King," built the logistics; the physics was the cargo — latent heat is the only form in which the nineteenth century could export winter. The household refrigerator replaced the trade in a generation, but the equation never retired: modern cold-chain containers and vaccine carriers still bank phase changes, now in engineered packs at tailored melting points, for exactly Tudor's reason.

Distillation: Paying L Over and Over

A still is a latent-heat treadmill: every kilogram of spirit in the bottle was vaporised at the boiler (paying water-ethanol L at the mix's rate) and condensed at the worm (being repaid the same, into cooling water), which is why distillation is among the most energy-hungry acts in the chemical kitchen and why vapour-recompression — recycling the condenser's repayment into the boiler's bill — is the industry's great economy. Desalination by distillation fights the same arithmetic at civilisational scale: 2.26 MJ per kilogram of water is the toll this page computes, and reverse osmosis won the market largely by refusing to pay it. L is small print with macroeconomic consequences.

Snowmaking and Other Industrial Winters

A ski resort's snow guns are latent-heat harvesters running in reverse weather: atomised water droplets must shed their 334 kJ/kg of fusion heat to the cold air in the seconds of their fall, which is why snowmaking has a wet-bulb temperature threshold (about −2 °C) below which the arithmetic closes and above which the guns make expensive rain. The mountain's whole artificial winter is scheduled by this page's constant against the forecast. The same ledger, sign reversed, sizes refrigeration plants and ice rinks: the compressor's job is to cart away L per kilogram of refrigerant circulated, a duty no capacity-only calculation can price.

Related Tools

More from the Physics Calculators hub: the Heat Capacity Calculator — the warming before and after the plateau — and the Newton's Law of Cooling Calculator for how the plateau's surroundings exchange heat over time.

Frequently Asked Questions

How much energy to take ice from −10 °C to steam at 110 °C?

Five legs, alternating the two pages of this wave: warm the ice (capacity, c_ice 2,090 × 10°), melt it (this page, 334 kJ/kg), warm the water (4,186 × 100°), vaporise it (this page again, 2,260 kJ/kg), warm the steam (c ≈ 2,000 × 10°). Per kilogram the sum is about 3.05 megajoules — and the striking audit is that the two phase changes (2.59 MJ) outweigh all three warmings combined (0.46 MJ) by more than five to one. Boiling a kettle dry costs far more than bringing it to the boil; the calculator pair prices the whole journey, leg by leg, exactly as a calorimetry examination would demand.

Why do farmers spray orchards with water before a frost?

To weaponise the reverse sign: water freezing on the blossoms releases its 334 kJ/kg as it turns to ice, and the freezing mixture holds the plant tissue at 0 °C — above the damage threshold of a hard frost's −4 °C air — for as long as unfrozen water remains arriving. The ice coat looks like the injury and is in fact the protection, a latent-heat blanket applied by hose. Citrus and strawberry growers run the numbers of this page on frost nights with real money on the table; the equation has saved more harvests than most pesticides.

Why does sweat cool, in these units?

Evaporation is vaporisation paid by the skin: each gram of sweat that evaporates (rather than dripping, which wastes the investment) carries off about 2.4 kJ at body temperature — the latent heat at skin temperature is a little higher than the 100 °C figure, 2,430 kJ/kg, a refinement worth knowing. A litre evaporated over an hour's hard exercise removes 2.43 MJ, a cooling power near 675 W, which is the only reason a body generating a kilowatt of metabolic heat in a marathon does not cook itself. Humidity defeats it by refusing the phase change — the air is already full — which is why humid heat is dangerous heat, a sentence this page can quantify.

What are phase-change materials in buildings?

Engineered latent stores: waxes and salt hydrates with melting points tuned near room temperature (20–26 °C), embedded in plasterboard or panels, which absorb daytime heat by melting (this page's Q, banked) and release it on the night air by freezing — flattening a room's temperature swing without machinery. A kilogram of good PCM banks about 200 kJ across its plateau — the equivalent, by the capacity page's arithmetic, of ten kilograms of concrete warmed through more than twenty degrees. The technology is Black's observation wearing a hard hat, and its specification sheets quote L in exactly this page's units.

Is latent heat really "heat" if temperature doesn't change?

It is energy transferred, stored as molecular potential energy (bond configuration) rather than kinetic (temperature) — the thermometer's silence measures only the kinetic ledger. The proof is the reversibility: freeze the water and every joule returns, measurably, in a calorimeter. Modern language prefers "enthalpy of fusion/vaporisation" for precision, but Black's "latent heat" survives because it names the experience honestly — the heat is there, hidden, and this calculator counts it whether or not any thermometer applauds.

Why does ice feel colder than cold water at the same temperature?

Because the ice is armed with this page's constant: held against skin, ice at 0 °C first absorbs 334 J per gram just to melt (without warming a degree), and only then begins absorbing as cold water — while water at 0 °C can only do the second. The numbing endurance of an ice pack is L at work on your hand, and the reason ice, rather than equally cold water, is the coolant of choice is the same: per gram delivered, its total absorption is the melt plus the warming, roughly double the water's over any useful range.

How is L measured?

By the method of mixtures or its electrical descendants: melt a known mass with a metered energy input inside a calorimeter and divide (for fusion), or condense a known mass of vapour and measure the heat it surrenders to a water bath (for vaporisation, the classic school experiment with its characteristically honest error bars). The values in this page's label — 334,000 and 2,260,000 J/kg for water — are among the most re-measured constants in school physics, and their durability across two centuries of apparatus is the usual tribute exact bookkeeping receives.