This article demonstrates the Bilinear Interpolation Calculator. Click here to learn more about our methodology.
You can access all calculators on the HVAC Calculators page or the ^^ drop-down menu above. The calculators are listed alphabetically by category.
Most of our calculators give the option to select metric or English units. For this calculator, as long as you stay consistent with units, you can use any units.
Example:
Suppose you want to calculate the Total Cooling Capacity of a 5-ton Bryant® package unit. A snippet of the equipment's performance data table at design conditions is provided. For our scenario, the design conditions are:
Condenser Entering Air Temperature: 79oF
Evaporator Entering Wet Bulb Temperature: 65oF
Solution:
This problem will be solved three times. Solution 1 will be to perform linear interpolation three times using Steps 1, 2, and 3 as described in the methodology section. Solution 2 will use the combined bilinear interpolation equation shown in Step 4 of the methodology section. Solution 3 will show how to use the calculator to quickly and accurately obtain the results.
For all solutions, the following inputs are below as provided in the table or given values:
P11 = 55.04 MBtuh
P12 = 59.00 MBtuh
P21 = 52.59 MBtuh
P22 = 56.34 MBtuh
x1 = 75oF
x2 = 85oF
y1 = 63oF
y2 = 67oF
x = 79oF
y = 65oF
Solution 1:
Step 1: Interpolate around point (x,y1)
R(x,y1) = P11(x2-x)/(x2-x1) + P21(x-x1)/(x2-x1)
= 55.04 (85-79)/(85-75) + 52.59 (79-75)/(85-75)
= 54.06 MBtuh
Step 2: Interpolate around point (x,y2)
R(x,y2) = P12(x2-x)/(x2-x1) + P22(x-x1)/(x2-x1)
= 59.00(85-79)/(85-75) + 56.34(79-75)/(85-75)
=57.936 MBtuh
Step 3 Perform a linear interpolation at point (x,y) using the results from Step 1 and Step 2:
R(x,y) = R(x,y1)(y2-y)/(y2-y1) + R(x,y2)(y-y1)/(y2-y1)
= 54.06(67-65)/(67-63) + 57.936(65-63)/(67-63)
=55.998 MBtuh
Solution 2:
The bilinear interpolation as a single equation as shown above:
R(x,y) = P11(x2-x)(y2-y)/((x2-x1)(y2-y1)) + P21(x-x1)(y2-y)/((x2-x1)(y2-y1)) + P12(x2-x)(y-y1)/((x2-x1)(y2-y1)) + P22(x-x1)(y-y1)/((x2-x1)(y2-y1))
R(x,y)=55.04(85-79)(67-65)/((85-75)(67-63))+52.59(79-75)(67-65)/((85-75)(67-63))+59.00(85-79)(65-63)/((85-75)(67-63))+56.34(79-75)(65-63)/((85-75)(67-63))
=55.998 MBtuh
Solution 3: To Solve using the calculator, enter the inputs in the same order they appear in the table. Below is a table showing the inputs. The result is shown in red in the middle of the table as 55.998MBtuh.
