Calculate blade pitch angle, radius, or pitch from any two values using meters, feet, inches, centimeters, degrees, or radians with unit conversion.

Blade Pitch Angle Calculator

Enter any 2 values to calculate the missing variable

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:

tan(theta) = P / (2*pi*r)

To calculate pitch angle:

theta = atan(P / (2*pi*r))

To calculate pitch:

P = 2*pi*r*tan(theta)

To calculate radius:

r = P / (2*pi*tan(theta))
  • 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.

theta = atan(P / (2*pi*r))
theta = atan(0.40 / (2*pi*0.50))
theta = 0.1269 rad = 7.27 deg

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°.

P = 2*pi*r*tan(theta)
P = 2*pi*12*tan(15 deg)
P = 20.20 in per rev

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.