Heat Transfer Calculator

Thermal conductivity (k) determines how readily a material conducts heat:

• copper 385 W/m·K
• aluminum 205
• steel 50
• glass 1.0
• brick 0.6-1.0
• wood 0.12-0.17
• fiberglass insulation 0.04
• aerogel 0.013

Lower k means better insulation. For a composite wall, total thermal resistance R_total = Σ(d/k) for each layer.

A wall with 1/2-inch drywall (R-0.45), 3.5-inch fiberglass batt (R-13), 1/2-inch plywood (R-0.63), and 1-inch foam board (R-5) has R_total ≈ 19. Heat flow Q = A × ΔT / R_total: for 200 sq ft of wall with 50°F temperature difference, Q = 200 × 50 / 19 = 526 BTU/hr.

Increasing insulation from R-13 to R-19 batts reduces heat loss by approximately 25%.

The convection coefficient h depends on fluid type, velocity, geometry, and whether flow is forced or natural. Typical values:

• natural convection in air 5-25 W/m²·K
• forced air (fan) 25-250
• water natural convection 100-1,200
• water forced convection 500-10,000
• boiling water 2,500-25,000

Electronic heat sinks rely on forced convection — a CPU generating 100W with a heat sink area of 0.01 m² and h = 100 W/m²·K (typical fan-cooled) produces a temperature rise of ΔT = Q/(hA) = 100/(100×0.01) = 100°C above ambient — explaining why high-performance CPUs need large heat sinks, heat pipes, or liquid cooling to maintain acceptable temperatures.

All objects emit thermal radiation proportional to T⁴ (absolute temperature in Kelvin). The Stefan-Boltzmann law gives power emitted: Q = εσAT⁴, where ε is emissivity (0 for perfect reflector, 1 for perfect blackbody), σ = 5.67×10⁻⁸ W/m²·K⁴.

A human body (surface area ≈ 1.7 m², skin temperature 33°C = 306K, ε ≈ 0.97) radiates approximately Q = 0.97 × 5.67×10⁻⁸ × 1.7 × 306⁴ = 817W. But it also absorbs radiation from surroundings — at room temperature (20°C = 293K), absorbed radiation is about 720W, so net radiation loss is approximately 97W (about 20% of resting metabolic heat output).

This is why you feel cold near windows in winter — the cold glass surface (5-10°C) radiates much less back to you than a warm wall, creating a net radiative heat loss that you perceive as a draft even without air movement.

To calculate conductive heat loss through a wall, use Fourier's law: Q = (k × A × ΔT) / d, where Q is the heat transfer rate in watts (W), k is thermal conductivity in W/m·K, A is area in m², ΔT is the temperature difference in kelvin (or degrees Celsius, since the interval is identical), and d is thickness in metres.

For example, a 0.2 m insulation layer with k = 0.04 W/m·K, A = 20 m², and ΔT = 25 °C gives Q = (0.04 × 20 × 25) / 0.2 = 100 W. Equivalently, using resistance: R = d/k = 5 m²·K/W, so Q = A × ΔT / R = 20 × 25 / 5 = 100 W. Both routes agree.

NIST publishes standard thermal-conductivity reference data used to validate these inputs.

Heat transfer rate (Q) is measured in watts (W), where 1 W = 1 joule per second, per the SI system maintained by the BIPM. Thermal conductivity (k) uses W/m·K, and the convection coefficient (h) uses W/m²·K.

Thermal resistance (R-value) is m²·K/W in SI, but building products in the US often quote imperial R-values in ft²·°F·hr/BTU. To convert, 1 SI R-value (m²·K/W) equals approximately 5.678 imperial R-value units. U-value (thermal transmittance) is the reciprocal, W/m²·K, so a U-value of 0.2 corresponds to R = 5 m²·K/W.

Because kelvin and Celsius share the same degree size, temperature differences are numerically identical in either. NIST and the SI brochure define these units precisely.

R-value and U-value are simple reciprocals: U = 1/R and R = 1/U. R-value (thermal resistance) measures how strongly a material resists heat flow, so higher is better for insulation; U-value (thermal transmittance) measures how easily heat passes through, so lower is better.

For example, a wall with R = 5 m²·K/W has U = 1/5 = 0.2 W/m²·K. When layers are stacked, add the R-values first: R_total = R1 + R2 + R3, then invert once at the end to get U_total.

Never average U-values directly for layers in series, because resistances add but transmittances do not. This reciprocal relationship, described in ASHRAE and Encyclopaedia Britannica references on building thermodynamics, underpins every building-envelope calculation.

To size heating and cooling equipment, engineers convert heat-loss rates into BTU per hour (BTU/hr). The conversion factor is 1 watt ≈ 3.412 BTU/hr, a value consistent with NIST energy-unit definitions. So a wall losing 100 W loses 100 × 3.412 = 341.2 BTU/hr.

In imperial form, heat loss is Q = U × A × ΔT with U in BTU/(hr·ft²·°F), A in ft², and ΔT in °F. A whole-house heat-load estimate sums losses through walls, windows, roof, floor, and air infiltration; HVAC contractors typically follow the ACCA Manual J method.

Oversizing equipment wastes energy and causes short-cycling, while undersizing fails on design-day extremes, which is why an accurate BTU/hr total matters before selecting a furnace or heat pump.

To find the insulation thickness needed to reach a target R-value, rearrange R = d/k into d = R × k, where d is thickness in metres, R is the target thermal resistance in m²·K/W, and k is the material's thermal conductivity in W/m·K.

For example, to reach R = 5 with fiberglass (k = 0.04 W/m·K), you need d = 5 × 0.04 = 0.2 m (20 cm). Switching to a higher-performance material lowers the required thickness: rigid polyisocyanurate (k ≈ 0.023) reaches the same R = 5 in d = 5 × 0.023 = 0.115 m (11.5 cm).

This is why compact assemblies favour low-k materials. Thermal-conductivity values should come from validated sources such as NIST or manufacturer test data per ASTM C518.

For heat conducted in series through stacked layers, total resistance is the sum of the individual resistances: R_total = R1 + R2 + ... + Rn, where each layer's R = d/k. You must also include interior and exterior air-film resistances, which HyperPhysics (Georgia State University) treats as additional series resistances.

Consider a wall of 0.012 m drywall (k = 0.17, R = 0.071), 0.09 m fiberglass (k = 0.04, R = 2.25), and 0.012 m plywood (k = 0.12, R = 0.10): R_total = 0.071 + 2.25 + 0.10 = 2.42 m²·K/W, giving U = 1/2.42 = 0.413 W/m²·K.

For parallel paths, such as studs beside insulation, resistances combine differently and thermal bridging through the framing lowers the effective assembly R-value.

Heat transfer analysis appears across nearly every engineering discipline. In building science, R-value and U-value calculations size insulation and meet energy codes such as those referenced by ASHRAE 90.1. In electronics, convection and conduction models keep CPUs, power transistors, and LED arrays below their junction temperature limits, a design practice detailed by IEEE thermal-management literature.

Automotive and aerospace engineers size radiators, intercoolers, and turbine cooling passages. Process industries design shell-and-tube heat exchangers using the log-mean temperature difference (LMTD) method. Even food safety and pharmaceutical cold chains depend on conduction and convection modelling to hold products within safe temperature bands.

Khan Academy and Encyclopaedia Britannica provide accessible primers on how these same three mechanisms scale from a coffee cup to a power plant.

• The most frequent error is mixing unit systems, for example combining SI thermal conductivity (W/m·K) with imperial area (ft2); always convert everything to one consistent set before computing.
• A second mistake is averaging U-values for layers in series instead of summing R-values first, which overstates insulation performance.
• Third, many estimates omit interior and exterior air-film resistances, understating real R-value.
• Fourth, people forget thermal bridging through studs, joists, and fasteners, which can cut a wall's effective R-value by 15 to 40 percent.
• Finally, radiation terms use absolute temperature in kelvin raised to the fourth power (T⁴), so using Celsius there produces large errors; always convert to kelvin before applying the Stefan-Boltzmann law.

NIST and BIPM unit guidance help prevent these slip-ups.