Infrared Thermography — Formula Reference

Consolidated formula sheet for IIRT Level 1 and Level 2 infrared thermography courses.

Level 1 Formulas

Converting temperatures between °C, °F, K, and °R for both absolute values and temperature differences.

Subtopic	Formula	Notes
Celsius → Kelvin (absolute)	T_K = T_°C + 273.15	Use absolute temperature in K for radiation equations.
Kelvin → Celsius (absolute)	T_°C = T_K − 273.15	Inverse of the Celsius → Kelvin conversion.
Celsius → Fahrenheit (absolute)	T_°F = (9/5)·T_°C + 32	Used when specifications are in °F.
Fahrenheit → Celsius (absolute)	T_°C = (5/9)·(T_°F − 32)	Convert nameplate data in °F to °C.
Kelvin → Rankine (absolute)	T_°R = (9/5)·T_K	Absolute temperature conversion used in some standards.
Rankine → Kelvin (absolute)	T_K = (5/9)·T_°R	Inverse of the Kelvin → Rankine conversion.
Fahrenheit → Rankine (absolute)	T_°R = T_°F + 459.67	Absolute scale based on Fahrenheit.
Rankine → Fahrenheit (absolute)	T_°F = T_°R − 459.67	Inverse of the Fahrenheit → Rankine conversion.
Temperature difference (°C ↔ K)	ΔT_K = ΔT_°C	Size of 1 K step equals 1 °C step.
Temperature difference (°C ↔ °F)	ΔT_°F = (9/5)·ΔT_°C	Use for relative differences (e.g. ΔT alarm limits).
Temperature difference (K/°C ↔ °R/°F)	ΔT_°R = ΔT_°F = (9/5)·ΔT_°C	All relative steps in °F and °R scale by 9/5 from °C/K.

Basic relationships between heat, temperature change, and material properties.

Subtopic	Formula	Notes
Heat Added/Removed	Q = m c ΔT	Q in joules; m in kg (or g); c in J/(kg·K) or J/(g·°C).
Specific Heat	c = Q / (m ΔT)	Defines how much heat is needed per unit mass per degree.
Heat Capacity	C_th = m c	Total heat needed to raise the whole object by 1 K or 1 °C.

Core energy and power relationships used in infrared thermography context.

Subtopic	Formula	Notes
Power	P = E / t	E: energy (J), t: time (s), P in watts.
kcal → J	1 kcal = 4184 J	Common conversion from food/heat tables.
cal → J	1 cal = 4.184 J	Small-scale heat calculations.
J → cal	1 J ≈ 0.239 cal	Inverse of cal → J.
BTU → J	1 BTU ≈ 1054 J	Used when HVAC data is in BTU.

Formulas for steady-state conductive heat flow and composite R-values.

Subtopic	Formula	Notes
Fourier’s Law (1-D)	Q̇ = k A (T₁ − T₂) / L	Q̇ in watts; k in W/(m·K); L in m; A in m².
Thermal Resistance (layer)	R = L / (k A)	R in K/W for a homogeneous layer.
Thermal Resistivity Form	R = ρ L / A (ρ = 1/k)	Alternative expression using material resistivity ρ.
Series Resistance	R_total = R₁ + R₂ + …	Sum internal, layers, and external film resistances.
Conduction via R-Value	Q̇ = ΔT / R_total	Direct way to estimate heat loss from known R-values.

Surface heat transfer between a solid and a moving fluid (air or liquid).

Subtopic	Formula	Notes
Newton’s Law of Cooling	Q̇ = h A ΔT	h in W/(m²·K); ΔT between surface and fluid temperature.

Radiative heat transfer relationships used in camera calibration and analysis.

Subtopic	Formula	Notes
Kirchhoff’s Law	A + R + T = 1	Emissivity (A or E), reflectivity (R), and transmissivity (T).
Stefan–Boltzmann (blackbody)	W_b = σ T⁴	W_b in W/m²; σ ≈ 5.67×10⁻⁸ W/(m²·K⁴).
Stefan–Boltzmann (greybody)	W = ε σ T⁴	ε is the surface emissivity (0–1).
Total Radiated Power	P = ε σ A T⁴	Multiply by area A to get total watts radiated.
Wien’s Displacement Law	λ_max = b / T	b ≈ 2.897×10⁻³ m·K; gives peak emission wavelength.

Angular conversions used for IFOV, mrad values, and lens comparisons.

Subtopic	Formula	Notes
Radians → Degrees	θ° = θ_rad × 180 / π	1 rad ≈ 57.3° (more precise than rounding to 60°).
mrad → Degrees	θ° ≈ θ_mrad × 0.0573	2.5 mrad ≈ 0.143°; used in IFOV calculations.