Mistake guide

Mixing degrees and radians on a calculator

The sine of 90 is 0.894.

01Assumption

The sine of 90 is 0.894.

02Actually

sin(90°) = 1. The value 0.894 is sin(90 rad), because 90 radians correspond to a multiple of 2π. 180° is exactly π radians, about 3.14159265358979.

03Why

Calculators and spreadsheets have a DEG/RAD switch that easily sits in the wrong position unnoticed. Because both modes return plausible numbers, the error often only shows up in the result.

04Check

Check the mode before any trigonometric function and compute a known value as a control: sin(30°) must give 0.5, cos(0) must give 1. If a result between −1 and 1 looks unexpected, suspect the mode first.

Matching conversions

Unit family: Angle

Sources

BIPM SI BrochureSI base units, prefixes and official SI context.
When not to use

Do not use as the sole basis for official, medical, safety-critical or contractual decisions.

Citation

Citation note: UnitCloud, mistake guide, sources reviewed: September 2026. Source basis: BIPM SI Brochure.