Choose heel height, horizontal run, or high heel angle and enter the other two values in cm or inches, with results in degrees or radians.
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High Heel Angle Formula
The high heel angle calculator uses a right-triangle model. Heel height is the vertical rise, horizontal run is the horizontal run, and the high heel angle is the angle between the foot and the ground.
- A = high heel angle
- H = heel height
- F = horizontal run
- tan = tangent function
- arctan = inverse tangent function
If you enter heel height and horizontal run, the calculator finds the angle using arctan(H / F). If you enter horizontal run and angle, it finds heel height using tan(A) * F. If you enter heel height and angle, it finds horizontal run using H / tan(A).
The calculator converts centimeters to inches when needed, and it converts degrees to radians for the trigonometry calculation. Results are then converted back to the unit you selected.
Estimated Heel Angles for a 24 cm horizontal run
The table below shows approximate angles for different heel heights using a 24 cm horizontal run.
| Heel Height | Formula | Approx. Angle |
|---|---|---|
| 3 cm | arctan(3 / 24) | 7.1ยฐ |
| 5 cm | arctan(5 / 24) | 11.8ยฐ |
| 7 cm | arctan(7 / 24) | 16.3ยฐ |
| 10 cm | arctan(10 / 24) | 22.6ยฐ |
| 12 cm | arctan(12 / 24) | 26.6ยฐ |
Unit Conversions Used
| Measurement | Conversion |
|---|---|
| Centimeters to inches | 1 cm = (1 / 2.54) in โ 0.393701 in |
| Inches to centimeters | 1 in = 2.54 cm |
| Degrees to radians | radians = degrees ร ฯ / 180 |
| Radians to degrees | degrees = radians ร 180 / ฯ |
Examples
Example 1: Find the high heel angle
You have a heel height of 7.5 cm and a horizontal run of 24 cm.
The high heel angle is approximately 17.35ยฐ.
Example 2: Find the heel height
You have a horizontal run of 9.5 inches and a high heel angle of 20ยฐ.
The heel height is approximately 3.46 inches.
FAQs
What does high heel angle mean?
High heel angle is the slope angle created by the heel height relative to the horizontal run. A higher heel height or a shorter horizontal run creates a larger angle.
Can you mix centimeters and inches?
Yes. You can enter heel height in centimeters and horizontal run in inches, or the reverse. The calculator converts the length units before applying the formula.
Is this the same as the exact angle of a real shoe?
It is an estimate based on a simple right triangle. Real shoes can vary because of platform height, sole thickness, arch shape, toe spring, and where the heel contacts the ground. For a basic comparison of heel height, horizontal run, and angle, the formula gives a useful approximation.
