Heat Transfer Calculator
Calculate heat energy using Q = mcΔT for basic heating/cooling, or heat transfer rate for conduction (Q = kAΔT/d) and convection (Q = hAΔT). See also our Thermal Expansion Calculator and Carnot Efficiency Calculator.
How to Calculate Heat Transfer
Heat transfer is the movement of thermal energy from a hotter object to a cooler one. There are three fundamental mechanisms: conduction (through solid materials), convection (through fluid motion), and radiation (through electromagnetic waves). Understanding heat transfer is essential for designing heating and cooling systems, insulation, engines, electronics cooling, and countless other engineering applications.
The basic heat equation Q = mcΔT calculates the total energy needed to change the temperature of a substance. Here, m is mass, c is specific heat capacity (energy per kg per degree), and ΔT is the temperature change. Water has an exceptionally high specific heat (4186 J/kg·K), which is why it takes a long time to boil water and why oceans moderate coastal climates.
For steady-state heat transfer through materials, Fourier's law of conduction gives the rate: Q̇ = kA(ΔT/d), where k is thermal conductivity, A is cross-sectional area, ΔT is temperature difference, and d is thickness. Materials with high k (metals) conduct heat well; materials with low k (insulation) resist heat flow. Newton's law of cooling describes convection: Q̇ = hAΔT, where h is the convective heat transfer coefficient.
Heat Transfer Formulas
Sensible Heat (temperature change):
Q = mcΔT
Conduction (Fourier's Law):
Q̇ = kA(T₁ - T₂)/d = kA(ΔT/d)
Convection (Newton's Law of Cooling):
Q̇ = hA(T_surface - T_fluid)
Radiation (Stefan-Boltzmann Law):
Q̇ = εσA(T₁⁴ - T₂⁴)
σ = 5.67×10⁻⁸ W/m²·K⁴
Thermal Resistance:
R_cond = d/(kA), R_conv = 1/(hA)
Q̇ = ΔT / R_total
Example Calculation
How much energy is needed to heat 1 kg of water from 20°C to 100°C?
Given: m = 1 kg, c = 4186 J/kg·K, ΔT = 80°C
Q = mcΔT = 1 × 4186 × 80 = 334,880 J
= 334.88 kJ = 80 kcal = 0.093 kWh
Time with a 2000W kettle:
t = Q/P = 334,880/2000 = 167.4 seconds ≈ 2.8 min
Note: This does not include the latent heat of
vaporization (2,260 kJ/kg) needed to actually boil water.
Material Properties Reference Table
| Material | c (J/kg·K) | k (W/m·K) | Notes |
|---|---|---|---|
| Water | 4186 | 0.606 | Highest c of common liquids |
| Ice | 2090 | 2.22 | Solid state |
| Steam | 2010 | 0.025 | At 100°C, 1 atm |
| Air | 1005 | 0.026 | At 20°C |
| Aluminum | 897 | 237 | Excellent conductor |
| Copper | 385 | 401 | Best common conductor |
| Iron/Steel | 449 | 80 | Moderate conductor |
| Glass | 840 | 1.0 | Poor conductor |
| Wood (oak) | 2380 | 0.17 | Good insulator |
| Concrete | 880 | 1.7 | Thermal mass |
| Fiberglass insulation | 700 | 0.04 | Excellent insulator |
| Styrofoam | 1200 | 0.033 | Best common insulator |
Frequently Asked Questions
What are the three modes of heat transfer?
The three modes are: (1) Conduction — heat transfer through direct molecular contact in solids or stationary fluids, driven by temperature gradients; (2) Convection — heat transfer by bulk fluid motion, either natural (buoyancy-driven) or forced (fan/pump-driven); (3) Radiation — heat transfer by electromagnetic waves, requiring no medium (works in vacuum). In most real situations, all three modes occur simultaneously, though one usually dominates.
What is specific heat capacity?
Specific heat capacity (c) is the amount of energy required to raise the temperature of 1 kg of a substance by 1°C (or 1 K). It is measured in J/(kg·K). Water has an unusually high specific heat (4186 J/kg·K) compared to metals (iron: 449, aluminum: 897). This means water absorbs and releases large amounts of energy with small temperature changes, making it excellent for heating systems, engine cooling, and climate regulation.
What is thermal conductivity?
Thermal conductivity (k) measures how well a material conducts heat, in W/(m·K). High k means good conductor: copper (401), aluminum (237), steel (50). Low k means good insulator: air (0.026), fiberglass (0.04), styrofoam (0.033). Metals conduct heat well because free electrons carry thermal energy. Insulators trap air in small pockets, exploiting air's low conductivity. The R-value of building insulation is the inverse of conductance: R = d/k.
What is the difference between heat and temperature?
Temperature is a measure of the average kinetic energy of molecules — it indicates how hot something is. Heat (Q) is the transfer of thermal energy between objects at different temperatures — it is energy in transit. A large lake at 20°C contains far more thermal energy than a cup of coffee at 80°C, even though the coffee is hotter. Heat always flows from higher to lower temperature. Temperature is measured in °C or K; heat is measured in joules or calories.
What is thermal resistance?
Thermal resistance (R) is the opposition to heat flow, analogous to electrical resistance. For conduction: R = d/(kA). For convection: R = 1/(hA). The heat transfer rate is Q̇ = ΔT/R, just like I = V/R in electricity. Resistances in series add: R_total = R₁ + R₂ + R₃. This makes it easy to analyze multi-layer walls — add the resistance of each layer (including air films on surfaces) to find total resistance and heat loss.
How does insulation work?
Insulation works by trapping air (or other gases) in small pockets within a low-conductivity matrix. Since still air has very low thermal conductivity (0.026 W/m·K), materials that prevent air circulation are excellent insulators. Fiberglass, foam, wool, and aerogel all work this principle. The key is preventing convection within the insulation — if air can circulate freely, it carries heat by convection, defeating the purpose. Thicker insulation provides more resistance (R = d/k).
Practical Applications
Heat transfer calculations are essential in building design (insulation, HVAC sizing, energy efficiency), electronics (CPU cooling, heat sinks), automotive (engine cooling, cabin heating), food processing (pasteurization, cooking times), and industrial processes (heat exchangers, furnaces, chemical reactors). Understanding heat transfer helps engineers design more efficient systems, reduce energy consumption, and prevent thermal failures in equipment.