Calculate blade pitch angle, radius, or pitch from any two values using meters, feet, inches, centimeters, degrees, or radians with unit conversion.
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Blade Pitch Angle Formula
The blade pitch angle is based on the relationship between pitch, radius, and the circumference traveled in one revolution. The core relationship is:
To calculate pitch angle:
To calculate pitch:
To calculate radius:
- theta = blade pitch angle
- P = pitch, or lead per revolution
- r = radius, measured from the hub or axis to the blade point being evaluated
- pi = 3.14159265…
- tan = tangent function
- atan = inverse tangent function
The calculator lets you enter any two values and solves for the missing one. If you enter radius and pitch, it calculates the pitch angle. If you enter radius and pitch angle, it calculates pitch. If you enter pitch and pitch angle, it calculates the radius where that angle applies.
Length units are converted internally so radius and pitch can be entered in meters, feet, inches, or centimeters. Angles can be entered or returned in degrees or radians.
Common Pitch Angle Relationships
The table below shows how the pitch-to-circumference ratio relates to pitch angle. The ratio is P / (2Ï€r).
| Pitch Angle | tan(theta) | Meaning |
|---|---|---|
| 5° | 0.0875 | Pitch is about 8.75% of the circular path at that radius. |
| 10° | 0.1763 | Pitch is about 17.63% of the circular path. |
| 15° | 0.2679 | A moderate pitch angle for many blade geometry checks. |
| 20° | 0.3640 | Pitch is about 36.40% of the circular path. |
| 30° | 0.5774 | A steeper pitch angle with much larger lead per revolution. |
Length Unit Conversions Used
| Unit | Meters Equivalent |
|---|---|
| 1 meter | 1 m |
| 1 foot | 0.3048 m |
| 1 inch | 0.0254 m |
| 1 centimeter | 0.01 m |
Example Calculations
Example 1: Calculate blade pitch angle
You have a radius of 0.50 m and a pitch of 0.40 m per revolution.
The blade pitch angle is approximately 7.27°.
Example 2: Calculate pitch
You have a radius of 12 in and a pitch angle of 15°.
The pitch is approximately 20.20 inches per revolution.
FAQ
What is blade pitch angle?
Blade pitch angle is the angle between the blade path around the hub and the helical path created by the pitch. In this calculator, pitch means the forward lead per full revolution. The angle depends on both the pitch and the radius where you measure it.
Why does radius matter for pitch angle?
The same pitch gives a different angle at different radii. Near the hub, the circular path is smaller, so the pitch angle is larger. Farther from the hub, the circular path is larger, so the same pitch produces a smaller angle.
Should pitch and radius use the same unit?
They need to be dimensionally consistent, but you do not have to enter them in the same unit. The calculator converts length values internally before applying the formula. For hand calculations, convert pitch and radius to the same length unit first.