Calculating Treadmill Gradient
Exercise treadmills are very popular pieces of gym training equipment, as they are simple to use. Sometimes they are too simple, and the treadmill incline settings built into the treadmill may not be clear or may not be accurate. The treadmill % incline or grade is not the same as the angle.
Here I outline how to measure the incline in percentage gradient (the standard measure) and also the gradient angle. The treadmill grade is basically a measure of the height distance for every 100 horizontal distance. e.g. A one-in-100 gradient = 1%, and a rise of 15 meters for every 100 meters is a 15% grade.
After using the following method to determine the actual gradient, you can compare this measure to the treadmill's displayed gradient, and determine how accurate it is. If the values are out, you may be able to create a conversion factor.
Measure The Gradient Using Basic Trigonometry
It does not matter which units you use, just make sure all measurement units are the same.
First, check that on the flat (zero) setting that the treadmill is in fact on the level. Take a measurement of the height of the roller or at the front and at the back. They should be the same. You can also use a builders spirit level (or a virtual level in a form of a phone app) to see if it is level.
Measure the distance between the front and the back roller, or between the front and back edge of the treadmill. It does not matter which point you choose, but the longer the distance should mean a more accurate measurement. Call this 'D'.
Now set the treadmill incline to the level you wish to measure. Again measure the height at the back and front of the treadmill. The front should be higher. Calculate the difference in heights (call this H).
As the treadmill was raised, the length of the horizontal run (L) would be decreased. The measurement L can be calculated using Pythagoras' Theorem (D2 = L2 + H2), solving for L.
L = √ (D2 - H2)
Now that you have height distance (H) and the length distance (L), you can calculate the percentage gradient (grade) as the ratio of H to L:
% gradient = H/L x 100
To calculate the angle of inclination the formula is arcsin(H/D)
A level/flat treadmill will have a grade of 0 percent. A 45 degree angle, when both H and L are the same, is equal to a gradient of 100 percent. A completely vertical but impossible treadmill would have a grade of infinity!
Converting between gradient and angle of inclination
To calculate gradient % from incline degrees, simply use the formula Tan(incline degrees)
e.g. for incline of 15degrees, enter tan(15) in a calculator, that comes about to be about 26.7% or 0.267
For vice-versa, calculating inclination degrees from gradient, the formula would be arctan(%grade / 100). You can type in Google: "arctan(%grade / 100) in degrees".
e.g. a 4% grade, "arctan(4/100) in degrees" returns 2.3 degrees. Check, "arctan(100/100) in degrees" returns 45 as expected.
Note: Tangent is just the ratio opposite/adjacent, or height/length. Measuring the treadmill is entirely unnecessary.
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