Calculate upper and lower angle limits from a nominal angle and ± tolerance, check a measured angle, or work back from limits in degrees or arcminutes.
Related Calculators
- Angle of Internal Friction Calculator
- Handrail Angle Calculator
- Interior Angle Calculator
- Exterior Angle Calculator
- Vertical Angle Calculator
- Central Angle Calculator
- All Construction Calculators
Angle Tolerance Formula
The calculator supports symmetric and asymmetric angular limits, direct numerical inspection, midpoint recovery from two limits, and the upper-deviation relationships below. Lower limit = nominal − lower deviation; upper limit = nominal + upper deviation. From two limits, midpoint = (lower + upper) / 2 and symmetric tolerance = (upper − lower) / 2. An original asymmetric nominal cannot be uniquely recovered from limits alone.
For unit conversion, the calculator uses:
- 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°.
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.
The tolerance is 0.1 radians.
Angle Tolerance Calculator FAQ
What does angle tolerance mean?
Angle tolerance specifies allowed deviations from a nominal angle. Symmetric tolerance uses the same magnitude on both sides; asymmetric tolerance uses separate lower and upper magnitudes. For nominal 60° ± 1.5°, the inclusive numerical limits are 58.5° to 61.5°. Direct PASS/FAIL output compares the entered measured number with these limits; measurement uncertainty, guard bands and any agreed conformity decision rule must be considered separately.
Does this calculator find the lower limit?
Yes. Select angular limits or inspection. For a symmetric tolerance, subtract the tolerance from nominal to find the lower limit:
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.
