Q = mcΔT
Last reviewed: January 2026
A calorimetry calculator computes heat transfer using the formula q = m times c times delta-T, where m is mass, c is specific heat capacity, and delta-T is the temperature change. It is used in chemistry and physics to analyze energy exchange in reactions and thermal processes.
Calorimetry measures heat transfer using the equation q = m × c × ΔT, where q is heat energy in joules, m is mass in grams, c is specific heat capacity, and ΔT is the temperature change.[1] Water is the standard calorimetric medium because of its unusually high specific heat capacity (4.184 J/g·°C), meaning it absorbs more heat per gram per degree than almost any other common substance.[2] In bomb calorimetry, used to measure food calories, a sample is combusted in an oxygen-rich chamber and the heat released is captured by surrounding water — 1 food Calorie equals 4,184 joules.[3] Use the Unit Converter for energy unit conversions.
Cooking: heating 1 kg of water from 20°C to 100°C requires Q = 1,000 × 4.186 × 80 = 334,880 J ≈ 335 kJ. This is why water takes much longer to heat than the same mass of metal. Climate science: water's high specific heat is why oceans moderate global temperatures — they absorb enormous heat with little temperature change. HVAC: calorimetry determines heating/cooling loads. Chemistry lab: coffee-cup and bomb calorimeters measure enthalpy of reactions.
| Substance | Specific Heat (J/g·°C) | State | Common Use |
|---|---|---|---|
| Water | 4.184 | Liquid | Reference standard |
| Ethanol | 2.44 | Liquid | Solvents, fuel |
| Aluminum | 0.897 | Solid | Cookware, cans |
| Iron/Steel | 0.449 | Solid | Construction |
| Copper | 0.385 | Solid | Wiring, pipes |
| Gold | 0.129 | Solid | Jewelry, electronics |
Calorimetry is the science of measuring heat transfer during chemical reactions, physical changes, and biological processes. The fundamental equation is q = mcΔT, where q is heat energy (in joules or calories), m is mass, c is specific heat capacity, and ΔT is the temperature change. When a hot object is placed in contact with a cold object in an insulated container (a calorimeter), heat flows from hot to cold until both reach the same temperature. The heat lost by the hot object equals the heat gained by the cold object, allowing calculation of unknown specific heat capacities, reaction enthalpies, and energy content of fuels and foods.
Specific heat capacity — the amount of energy required to raise one gram of a substance by one degree Celsius — varies enormously across materials. Water has one of the highest specific heat capacities of any common substance at 4.184 J/(g·°C), which is why it takes so long to boil water but also why oceans moderate coastal climates. Metals have much lower specific heat capacities: aluminum is 0.897, iron is 0.449, and copper is 0.385 J/(g·°C). This means a gram of copper heats up 10.9 times faster than a gram of water for the same energy input, which is why metal pans get hot quickly while the water inside them heats slowly.
A coffee-cup calorimeter (constant-pressure calorimeter) is the simplest design: two nested polystyrene cups with a lid, thermometer, and stirrer. It measures enthalpy changes for reactions occurring in aqueous solution at atmospheric pressure. Dissolving ammonium nitrate in water (an endothermic process used in instant cold packs) causes the water temperature to drop, and measuring that drop with q = mcΔT yields the enthalpy of dissolution. The main limitation is heat loss to the surroundings — polystyrene provides decent insulation but is imperfect, introducing errors of 5-15% compared to more sophisticated instruments.
A bomb calorimeter measures the energy content of fuels and foods by burning a sample in a sealed, oxygen-pressurized steel vessel (the "bomb") submerged in a known mass of water. The temperature rise of the water indicates the heat released by combustion. Food calorie values on nutrition labels are determined using bomb calorimetry — a sample of the food is dried, compressed into a pellet, and combusted completely. The result is gross energy; the body does not extract 100% of this energy because digestion is incomplete and some energy is lost in urine and feces. The Atwater system adjusts bomb calorimetry values to physiological values: 4 calories per gram of protein, 4 per gram of carbohydrate, 9 per gram of fat, and 7 per gram of alcohol.
Differential scanning calorimetry (DSC) measures heat flow into or out of a sample as temperature changes at a controlled rate. This technique detects phase transitions (melting, crystallization, glass transitions), measures reaction kinetics, and characterizes material purity. Pharmaceutical companies use DSC to verify drug polymorphism — the same chemical compound can crystallize in different structures that melt at different temperatures and may have different bioavailability. A drug that unexpectedly converts to a less soluble polymorph during storage could become therapeutically ineffective, making DSC testing a critical quality control step.
Isothermal titration calorimetry (ITC) measures the heat released or absorbed when two solutions are mixed incrementally, providing direct thermodynamic characterization of molecular interactions. Drug discovery uses ITC to measure how tightly a candidate drug molecule binds to its target protein — the binding constant, enthalpy, and entropy of interaction are all obtained from a single experiment. This thermodynamic profile helps predict drug efficacy and selectivity. ITC is also used in food science to study protein-polysaccharide interactions, in materials science to characterize surfactant behavior, and in environmental chemistry to study contaminant binding to soil particles.
Every calorimetry measurement contains systematic and random errors that must be understood and, where possible, corrected. The largest systematic error in simple calorimeters is heat exchange with the surroundings — an exothermic reaction heats the calorimeter water, and that warmed water immediately begins losing heat to the room. The temperature you measure at any given moment is lower than the theoretical maximum because some heat has already escaped. Extrapolation methods (plotting temperature versus time and extrapolating back to the moment of mixing) correct for this heat loss and can improve accuracy by 10-20%. More sophisticated adiabatic calorimeters actively adjust their jacket temperature to match the reaction vessel, eliminating heat loss almost entirely.
The heat capacity of the calorimeter itself (the "calorimeter constant") must be included in calculations for precise work. When a reaction releases heat, some of that energy warms the water and some warms the calorimeter walls, stirrer, and thermometer. Ignoring the calorimeter constant underestimates the true heat released. The calorimeter constant is determined by calibration — typically by running a reaction with a known enthalpy of reaction (such as neutralizing a strong acid with a strong base) or by using an electrical heater to deliver a precisely known amount of energy and measuring the resulting temperature change.
See also: Density Calculator · Ideal Gas Law Calculator · Temperature Converter
→ Water's specific heat is unusually high. At 4.184 J/g·°C, water absorbs or releases far more energy per degree than most substances. This is why water is used as a coolant, why coastal climates are moderate, and why a pot of water takes so long to boil compared to the metal pot it's in.
→ q = mcΔT only works without phase changes. This formula calculates sensible heat — temperature change within a single phase. If ice is melting or water is boiling, you need latent heat calculations (q = mL) instead. Phase changes absorb or release energy without changing temperature.
→ In calorimetry problems, heat lost equals heat gained. For a hot object placed in cold water: m₁c₁ΔT₁ = m₂c₂ΔT₂ (assuming no heat loss to surroundings). This is how unknown specific heats are determined experimentally. Real calorimeters have correction factors for heat loss to the container.
→ Convert carefully between calories and joules. 1 calorie (thermochemical) = 4.184 joules. Food "Calories" (capital C) are actually kilocalories — 1 food Calorie = 1,000 thermochemical calories = 4,184 joules. See our Unit Converter for energy conversions and our Calorie Calculator for nutrition.
See also: Unit Converter · Temperature Converter · Energy Converter · Scientific Calculator