Heat Transfer Calculator | Conduction, Convection & Radiation
Calculate heat transfer by Fourier conduction, Newton convection, Stefan-Boltzmann radiation, or Q=mcΔT sensible heat. Material presets, NIST constants, step-by-step working.
| Copper | 401 | |
| Aluminum | 237 | |
| Steel (carbon) | 50 | |
| Glass | 1.05 | |
| Concrete | 0.8 | |
| Wood (pine) | 0.12 | |
| Air (25°C) | 0.0262 | |
| Insul. foam | 0.03 | |
| Water (25°C) | 0.607 |
Press Enter to calculate · Esc to reset
What Is the Heat Transfer Calculator | Conduction, Convection & Radiation?
Heat transfer is the movement of thermal energy from one system to another due to a temperature difference. There are three fundamental mechanisms, conduction, convection, and radiation, each governed by a distinct formula.
Conduction (Fourier's Law)
Q = kA(T₁-T₂)/L describes heat flow through a solid material. k is the thermal conductivity (higher = better conductor), A is the cross-sectional area, ΔT is the temperature difference, and L is the thickness. Copper (k=401) conducts about 13,000 times better than insulation foam (k=0.03).
Convection (Newton's Law of Cooling)
Q = hA(Tₛ-T∞) describes heat transfer between a solid surface and a moving fluid. h is the convective heat transfer coefficient, which depends on fluid properties, velocity, and geometry. Typical values: still air h≈5 W/(m²·K), forced water h≈1000 W/(m²·K).
Radiation (Stefan-Boltzmann Law)
Q = εσA(T₁&sup4;-T₂&sup4;) uses the Stefan-Boltzmann constant σ = 5.670374419×10⁻⁸ W/(m²·K&sup4;) (NIST 2018 CODATA exact value). Temperatures must be in Kelvin. ε is emissivity (0=perfect reflector, 1=blackbody).
Sensible Heat
Q = mcΔT describes the heat required to change the temperature of a substance without a phase change. c is the specific heat capacity in J/(kg·K). For water, c = 4186 J/(kg·K).
Formula
How to Use
- 1Select a heat transfer mode: Conduction (Fourier), Convection (Newton), Radiation (Stefan-Boltzmann), or Sensible Heat.
- 2Use a preset (Wall insulation, Copper pipe, Glass window, Water heating, Oven radiation) to autofill a scenario.
- 3For Conduction: select a material from the dropdown to autofill the thermal conductivity k value.
- 4For Sensible Heat: select a material from the dropdown to autofill the specific heat capacity c.
- 5Enter the remaining required values (area, temperatures, thickness/mass).
- 6Temperatures can be in °C for conduction, convection, and sensible heat. Radiation requires °C input and auto-converts to Kelvin.
- 7Press Calculate (or Enter) to see the heat transfer rate Q in Watts or heat energy Q in Joules.
- 8Expand Step-by-step to see the full substituted calculation with all intermediate values and unit labels.
Example Calculation
A foam insulation wall: k = 0.03 W/(m·K), A = 10 m², T₁ = 20°C, T₂ = -10°C, L = 0.1 m.
Q = 0.03 × 10 × (20-(-10)) / 0.1 = 0.03 × 10 × 30 / 0.1 = 90 W.
90 W of heat is lost through the wall, equivalent to a single incandescent bulb.
Heating 2 kg of water from 20°C to 100°C: m = 2 kg, c = 4186 J/(kg·K), ΔT = 80°C.
Q = 2 × 4186 × 80 = 669,760 J = 669.76 kJ ≈ 160 kcal.
An oven surface: ε = 0.9, A = 0.5 m², T₁ = 250°C (523 K), T₂ = 25°C (298 K).
Q = 0.9 × 5.67×10⁻⁸ × 0.5 × (523&sup4; - 298&sup4;) ≈ 2,290 W.
Understanding Heat Transfer | Conduction, Convection & Radiation
This calculator runs entirely in your browser, no data is sent to any server. Thermal conductivity and specific heat values shown in reference tables are sourced from NIST Standard Reference Data (SRD 10). The Stefan-Boltzmann constant uses the NIST 2018 CODATA exact value: 5.670374419×10⁻⁸ W/(m²·K&sup4;).
Engineering Applications
- • Building insulation design: Fourier conduction used to calculate R-values and heat loss through walls, roofs, and windows.
- • HVAC systems: convection equations size heat exchangers, radiators, and fin arrays.
- • Electronics cooling: both conduction (thermal interface materials) and convection (heatsinks, fans) are critical.
- • Chemical engineering: calorimetry and sensible heat calculations for reactor design and process heat balances.
- • Astrophysics and industrial furnaces: Stefan-Boltzmann radiation dominates at very high temperatures.
Understanding the Three Modes
In most real-world scenarios, all three modes occur simultaneously. A hot pipe loses heat by conduction through the pipe wall, convection from the outer surface to air, and radiation from the surface to surroundings. Engineers calculate each contribution separately and sum them for total heat loss.
Frequently Asked Questions
What is the difference between heat and temperature?
Heat (Q) is thermal energy transferred between objects; temperature (T) is a measure of the average kinetic energy of molecules.
- • A large cold object can contain more thermal energy than a small hot object
- • Heat always flows from higher temperature to lower temperature (second law)
- • Heat is measured in Joules (J) or calories; temperature in °C, °F, or Kelvin (K)
What is thermal conductivity and what materials have high k values?
Thermal conductivity k measures a material's ability to conduct heat in W/(m·K).
- • Copper: 401, Aluminum: 237, Steel: 50
- • Glass: 1.05, Water: 0.607, Concrete: 0.8
- • Wood: 0.12, Air: 0.026, Foam: 0.03
Metals have high k (good conductors); gases and foams have very low k (good insulators).
Why does the radiation formula use temperature in Kelvin?
The Stefan-Boltzmann law Q = εσA(T₁⁴-T₂⁴) requires absolute temperature in Kelvin because it involves T⁴.
- • Kelvin = °C + 273.15
- • Using °C would give incorrect results since 0°C does not represent zero thermal energy
- • This calculator auto-converts your °C input to Kelvin for the calculation
What is emissivity and how do I choose the right value?
Emissivity (ε) is a dimensionless ratio from 0 to 1 that describes how efficiently a surface emits radiation compared to a perfect blackbody.
- • Blackbody: ε = 1 (perfect emitter/absorber, theoretical)
- • Matte black paint: ε ≈ 0.95 to 0.98
- • Human skin: ε ≈ 0.95 to 0.99
- • Polished aluminum: ε ≈ 0.03 to 0.05 (low emission, good reflector)
- • Oxidized steel: ε ≈ 0.80 to 0.85
How does the convective heat transfer coefficient h relate to air speed?
The convective coefficient h increases significantly with fluid velocity:
- • Still air (free convection): h ≈ 5–10 W/(m²·K)
- • Forced air (fan): h ≈ 20–100 W/(m²·K)
- • Still water: h ≈ 200–500 W/(m²·K)
- • Flowing water: h ≈ 1000–15,000 W/(m²·K)
What is specific heat capacity and why does water have a high value?
Specific heat c is the energy required to raise 1 kg of a substance by 1 K.
- • Water c = 4186 J/(kg·K), among the highest of common substances
- • High c means water is an excellent thermal buffer and coolant
- • Water's high c arises from hydrogen bonding between molecules
- • Steel c = 490 J/(kg·K), heats up much faster than water per kilogram
What is an R-value and how does it relate to Fourier conduction?
The R-value is thermal resistance: R = L / k in SI units (m²·K/W).
- • Fourier conduction: Q = A × ΔT / R
- • Higher R-value = better insulation (less heat transfer per °C difference)
- • R-values in US building codes use imperial units (h·ft²·°F/BTU)
- • Layers in series add their R-values: R_total = R₁ + R₂ + ...
When does radiation become the dominant mode of heat transfer?
Radiation dominates at very high temperatures because Q scales with T⁴:
- • At room temperature (~300 K), radiation is typically small compared to conduction/convection
- • In vacuum (space), radiation is the only mode of heat transfer
- • Industrial furnaces above 600°C: radiation becomes the primary mechanism
- • Solar energy (5778 K sun surface) reaches Earth almost entirely by radiation