Calculate propeller angle, pitch, or diameter from any two values in one calculator with support for degrees, radians, inches, and millimeters.
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Propeller Angle Formula
The propeller angle relates pitch to the circumference swept by the propeller diameter. The calculator uses any two known values to solve for the missing value.
theta = arctan(P / (pi*D))
P = tan(theta) * pi*D
D = P / (pi*tan(theta))
- theta = propeller angle, in radians inside the trigonometric functions
- P = propeller pitch
- D = propeller diameter
- pi = approximately 3.14159
If you enter pitch and diameter, the calculator solves for propeller angle using the arctangent formula. If you enter angle and diameter, it solves for pitch. If you enter angle and pitch, it solves for diameter. Pitch and diameter must use the same length basis in the formula, so the calculator converts inches and millimeters as needed.
Common Unit Conversions for Propeller Angle Calculations
| Conversion | Multiplier | Use |
|---|---|---|
| Millimeters to inches | mm × 0.0393701 | Convert pitch or diameter to inches |
| Inches to millimeters | in × 25.4 | Convert a calculated length back to mm |
| Degrees to radians | degrees × pi / 180 | Use angle in tangent formulas |
| Radians to degrees | radians × 180 / pi | Display angle in degrees |
Typical Propeller Angle Ranges
| Angle | General meaning |
|---|---|
| Low angle | Lower pitch relative to diameter |
| Medium angle | Balanced pitch-to-diameter relationship |
| High angle | Higher pitch relative to diameter |
Example Propeller Angle Calculations
Example 1: Calculate propeller angle
Suppose the propeller pitch is 10 inches and the propeller diameter is 12 inches.
theta = arctan(10 / (pi*12))
theta = 0.2596 radians = 14.874 degrees
The propeller angle is about 14.87 degrees.
Example 2: Calculate propeller pitch
Suppose the propeller angle is 15 degrees and the propeller diameter is 12 inches.
15 degrees = 0.2618 radians
P = tan(0.2618) * pi*12
P = 10.101 inches
The propeller pitch is about 10.10 inches.
Propeller Angle Calculator FAQ
What is propeller angle?
Propeller angle is the angle formed by the propeller pitch relative to the circumference based on the propeller diameter. In this calculation, pitch is compared to pi × diameter, which represents one full circumference at that diameter.
Does pitch need to be in the same unit as diameter?
Yes. Pitch and diameter must be in the same length unit before applying the formula. If pitch is in inches and diameter is in millimeters, one value has to be converted first. The calculator handles inch and millimeter conversions for you.
Why are radians used in the formula?
Trigonometric formulas such as tangent and arctangent use radians as the standard angle measure. You can still enter or read the angle in degrees, but the angle is converted to radians when used inside the formula.