Calculate nominal angle, tolerance, or upper limit from any two values in degrees or radians with this angle tolerance calculator.

Angle Tolerance Calculator

Enter any 2 values to calculate the missing variable

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Angle Tolerance Formula

The angle tolerance calculator uses the upper tolerance relationship between a nominal angle, an allowed tolerance, and the upper limit.

U = N + T
N = U - T
T = U - N

For unit conversion, the calculator uses:

degrees = radians * 57.2958
radians = degrees * 0.0174533
  • U = upper limit angle
  • N = nominal angle
  • T = tolerance
  • degrees = angle measured in degrees
  • radians = angle measured in radians

If you enter the nominal angle and tolerance, the calculator adds them to find the upper limit. If you enter the upper limit and tolerance, it subtracts the tolerance to find the nominal angle. If you enter the upper limit and nominal angle, it subtracts the nominal angle from the upper limit to find the tolerance.

The calculator converts all entered values to degrees before calculating, then converts the missing value back to the unit selected for that field.

Angle Unit Conversions and Common Reference Values

Use these values to check whether your angle input or result is in the expected unit.

Degrees Radians Common description
1° 0.0174533 rad Small angle
30° 0.523599 rad Common drafting angle
45° 0.785398 rad Half of a right angle
90° 1.5708 rad Right angle
180° 3.14159 rad Straight angle
Known values Missing value Use this relationship
Nominal angle and tolerance Upper limit Upper limit = nominal angle + tolerance
Upper limit and tolerance Nominal angle Nominal angle = upper limit – tolerance
Upper limit and nominal angle Tolerance Tolerance = upper limit – nominal angle

Angle Tolerance Examples

Example 1: Calculate the upper limit

You have a nominal angle of 45° and a tolerance of 2°.

U = N + T
U = 45 + 2 = 47°

The upper limit is 47°.

Example 2: Calculate the tolerance

You have an upper limit of 1.6 radians and a nominal angle of 1.5 radians.

T = U - N
T = 1.6 - 1.5 = 0.1 rad

The tolerance is 0.1 radians.

Angle Tolerance Calculator FAQ

What does angle tolerance mean?

Angle tolerance is the allowed variation from a nominal angle. In this calculator, the tolerance is treated as the amount added to the nominal angle to get the upper limit. For example, if a nominal angle is 60° with a tolerance of 1.5°, the upper limit is 61.5°.

Does this calculator find the lower limit?

No. This calculator is set up for the upper limit only. If you need the lower limit for a symmetric tolerance, subtract the tolerance from the nominal angle:

Lower Limit = Nominal Angle - Tolerance

Can I mix degrees and radians?

Yes. You can enter one value in degrees and another in radians. The calculator converts the entered values to degrees, performs the calculation, then returns the missing value in the unit selected for that field.