What is this converter?
Converts an angle between degrees, radians, and gradians. All conversions pass through the radian, the SI unit of plane angle.
Use it when:
- A programming language's trigonometric functions expect radians but your data is in degrees.
- A surveying instrument reports gradians.
- You need an exact conversion rather than a remembered approximation.
Intended for: Developers, surveyors, engineers, and students of trigonometry.
How is this calculated?
- Each supported unit is defined by a fixed conversion factor relative to one base unit for the quantity (for example, the metre for length).
- The value you enter is first converted from the source unit into that base unit by multiplying by the source unit's factor.
- The base value is then converted into the target unit by dividing by the target unit's factor.
- Because both factors are exact constants, the conversion is a single deterministic multiplication and division — the same input always produces the same output.
Formula
Degrees to radians
radians = degrees × π / 180
A full turn is 360 degrees or 2π radians, which fixes the ratio.
Example
Converting 90 degrees to radians.
- 90 × π ÷ 180 = π/2.
- π/2 ≈ 1.5708.
Result: 90 degrees ≈ 1.5708 radians (exactly π/2), or 100 gradians.
Frequently asked questions
Why do programming languages use radians?
Because the calculus of trigonometric functions is simplest in radians — the derivative of sin(x) is cos(x) only when x is in radians. Almost every standard library follows that convention.
What is a gradian?
A unit dividing a right angle into 100 parts, so a full turn is 400 gradians. It survives mainly in surveying, where decimal subdivision of a right angle is convenient.
Assumptions
What this converter takes as given:
- Conversion factors are the internationally standardised definitions of each unit, not regional or historical variants.
- The value you enter is treated as an exact quantity — no measurement uncertainty is carried through the conversion.
- Results are rounded only for display; the underlying arithmetic uses full precision.
Limitations
What this converter cannot know or does not model:
- The converter does not know the precision of your original measurement, so it cannot report significant figures for you.
- Units that share a name but differ by region or era (for example, different definitions of a gallon or a ton) are offered only in the variants listed in the unit menu.
- Very large or very small magnitudes are subject to the limits of double-precision floating-point arithmetic.
- Because π is irrational, degree-to-radian results are shown to finite precision; only the underlying arithmetic is exact.