Radiant Heating & Cooling Calculators

NOTE: For determining the amount of heating or cooling that can be provided by a radiant source, we have developed the following calculators. While they eliminate a chalkboard full of equations, it is important to understand how to use them and what the outputs mean. Feel free to play around with them but we suggest to have the Chiltrix engineering dept. comment/assist before you rely upon any calculations.

  1. The first calculator “RADIANT” calculates the net radiant transfer per ft.^2 based on the emissivity and temperature of the radiant surface and, of the surfaces of the room to be heated or cooled. The radiant transfer values must be added to convection values to get a total transfer value. Note that all objects in the universe (>0 degrees K) continuously emit radiant energy. And all objects continuously absorb radiant energy. The calculator calculates and compares both the absorbtion and emission to provide the net energy transfer.
  2. The 2nd calculator is for CONVECTION, as with the radiant calculator, this is not the full heating or cooling calculation, as the output will then need to be added to the results of the radiant calculator to get a total value.
  3. The 3rd calculator, SURFACE TEMP, can be used to calculate a surface temperature based on a heating or cooling source (heat transfer plate temperature) and an R value of the materials that separate the room facing surface and the source.
  4. The 4th calculator, CONVERT K TO R, allows you to find the R value of a material. While only some materials will have a published R value, nearly all materials will have a K value that can be found online. This calculator converts a K value to an R value.
  5. The 5th calculator, DEW POINT, allows a calculation of dew point from a known RH% and temperature. This is important for understanding radiant cooling capacity of a system under various conditions.

TIP: The CXRC Radiant Cooling Calculator manual includes a tutorial with additional info on how to use these calculators: CXRC1 Radiant Cooling Controller Manual

TIP: In most climates, radiant cooling will need a dehumidifier in order to provide best comfort, and, to keep the dew point low enough to obtain maximum radiant cooling capacity. Note that radiant cooling generally requires a dew point controller to prevent unwanted condensation.

Radiant Calculator (Stefan-Boltzmann)
Calculates net radiant heat exchange between a radiant panel and room surfaces using the Stefan-Boltzmann law: Q = e · σ · T⁴
Radiant Panel Emissivity e
Radiant Surface Temperature °F
Area (fixed at 1 m² for per-unit calc)
Q = e · σ · T⁴ · Area
W/m²

Material Surface Emissivity e
Avg. Room Surface Temperature °F
Area
1.00
Q = e · σ · T⁴ · Area
W/m²

Net Radiant Output
W *
Net Radiant Output
BTU/hr *
Net Radiant Output
BTU/ft² *
* Negative = cooling  |  Positive = heating
Important: Add Radiant Output to Convection Output for the total value. See Convection Calculator (Tab 2).
Convection Calculator — Heating / Cooling
For wall, floor, or ceiling radiant surfaces. Select function, enter inputs in blue. Natural convection using Grashof / Rayleigh / Nusselt correlations.
Select Function
Inputs
Air Temp (T∞) °F
20.00
°C
Surface Temp (Tw) °F
29.44
°C
Area of Surface (A) ft²
18.58
Perimeter (P) ft
18.29
m
Wall Height (if wall) ft
2.74
m

Air Properties
Air Density (ρ) kg/m³
Air Viscosity (μ) N·s/m²
Specific Heat (Cp) J/g·K
Thermal Conductivity (k) J/s·m·K
Intermediate Calculations
Film Temp (Tf)
°C
ΔT (Temp diff)
°C
Abs. Film Temp (Tf)
°K
Prandtl Number (Pr)
L = A/P
m
Thermal Exp. (β)
K⁻¹
Grashof No. (Gr)
Rayleigh No. (Ra)
h (used)
W/m²·K

Convective Output — Floor / Wall / Ceiling
Area
h (coeff.)
W/m²·K
ΔT
°C
Capacity W
Watts
Capacity BTU
BTU/hr
BTU / ft²
BTU/hr·ft²
Solving For Surface Temp
Calculates the indoor surface temperature (Th) given the radiant source temperature, indoor air temperature, and R-value of the separating construction.
Tc Radiant Source Temp PEX / Heat Exchanger °F
Ta Indoor Air Temp Indoor room air °F
R Total R Value R-Value (Tc → Ta)
U U Value (= 1/R)

Th Indoor Surface Temp
°F
°C shown on right
Formula: Th = (R · Ta + Tc) / (1 + R)
where R is the total R-value separating the radiant source from the indoor air.
Calculator for Converting K-value to R-value
Converts thermal conductivity (K-value in W/m·K) to U-value and R-value in imperial units.
Input K = (W/m·k)
U = BTU·in / (hr·ft²·°F)
R per inch

Input Inches (thickness)
R-Value Total
Formulas:
U (BTU·in/hr·ft²·°F) = K × 693.81 / 100
R per inch = 1 / U
R-Value Total = R per inch × thickness (inches)
Dew Point Calculator
Calculates the dew point temperature from dry-bulb temperature and relative humidity using the Magnus formula.
Input Temperature °F
Relative Humidity %

Output Dew Point
°F
Dew Point (°C)
°C
Magnus Formula:
Td = 243.04 × [ln(RH/100) + 17.625·T/(243.04+T)] / [17.625 − ln(RH/100) − 17.625·T/(243.04+T)]
where T is in °C and Td is the dew point in °C.
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