Measure the long side and designate it as "x." For example, assume it is 36 inches long.
Measure the short side and designate it as "y." For example, assume it is 6 inches long.
Multiply 12 times the fourth power of x. In our example, 36 to the fourth power is 1,679,616, which when multiplied by 12 equals 20,155,392.
Divide the fourth power of y by your result from Step 3. In our example, 6 to the fourth power is 1,296, and 1,296/20,155,392 = 0.0000643
Subtract your result from Step 4 from 1. In our example, 1 - 0.0000643 = 0.9999367
Divide y by x and multiply the result by 0.21. In our example, 6 / 36 * 0.21 = 0.035
Multiply your results from Steps 5 and 6 together. In our example, 0.035 * 0.9999367 = 0.03499.
Subtract your result from Step 7 from 1/3. In our example, 1/3 - 0.03499 = 0.29834.
Multiply the value of x by the value of y-cubed. In our example, 6 to the third power is 216, which when multiplied by 36 equals 7,776.
Multiply your results from Steps 8 and 9 together to get the torsional constant for your beam. In our example, 7,776 * 0.29834 gives us a torsional constant of 2,319.89.