Angle ConverterFree online other calculator — instant results, no sign-up
Convert standard angle units.
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About the Angle Converter
The Angle Converter converts angle values between degrees, radians, and gradians. Select the starting and target units to express the same angle on a different scale. With the default settings, it converts 1 degree to 1.111111 gradian.
- Value
- The numerical angle to convert, measured in the selected From unit; the default is 1.
- From
- The unit of the entered angle—degree, radian, or gradian—with degree selected by default.
- To
- The unit for the converted angle—gradian, radian, or degree—with gradian selected by default.
Formula and method
y = x × (C_to / C_from), where C_degree = 360, C_radian = 2π, and C_gradian = 400. For the default inputs: y = 1 × (400 / 360) = 10/9 gradian ≈ 1.111111 gradian.
- xThe entered Value, expressed in the From unit.
- yThe converted angle, expressed in the To unit.
- C_fromThe number of source units in one full turn.
- C_toThe number of target units in one full turn.
- C_degree360 degrees per full turn.
- C_radian2π radians per full turn.
- C_gradian400 gradians per full turn.
- πPi, the mathematical constant equal to a circle’s circumference divided by its diameter.
The calculation uses the equivalence of 360 degrees, 2π radians, and 400 gradians in a full turn. It divides the target unit’s full-turn count by the source unit’s full-turn count, then multiplies the entered value by that ratio. For degree to gradian, the ratio is 400/360; multiplying by the default value of 1 gives 10/9 gradian, displayed as 1.111111 gradian.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Value1
- Fromdegree
- Togradian
Results
- Result1.111111 gradian
How to use the Angle Converter
- 1Enter the angle in Value; leave it at 1 to follow the default example.
- 2Select degree in From to indicate that the entered angle is in degrees.
- 3Select gradian in To to request the result in gradians.
- 4Read the Result row: the default inputs produce 1.111111 gradian.
Reading your result
The Result row shows the converted numerical value followed by the target unit. In the default example, Result = 1.111111 gradian means that 1 degree and approximately 1.111111 gradian represent the same angle. The conversion changes the unit, not the angle’s size.
Limitations
This tool covers only degrees, radians, and gradians; it does not directly convert degrees-minutes-seconds notation or angular rates. Displayed decimals may be rounded: the default result is exactly 10/9 gradian before rounding. The conversion formula preserves negative signs and angles larger than a full turn rather than normalizing them to a single rotation. Converting units does not improve the precision of the original measurement.
Common questions
Why does 1 degree become 1.111111 gradian?+
A full turn contains 360 degrees but 400 gradians, so each degree equals 400/360, or 10/9, gradian. The default result rounds this repeating decimal to 1.111111 gradian.
What is the difference between a radian and a gradian?+
A radian is defined by an arc whose length equals the circle’s radius, giving 2π radians per full turn. A gradian divides a full turn into 400 equal parts.
What happens if From and To use the same angle unit?+
The conversion ratio is 1, so the numerical value stays unchanged and the result retains that unit.
Does converting an angle wrap it into one full turn?+
No. Unit conversion scales the angle without removing complete turns. Finding an equivalent angle within a single rotation is a separate normalization operation.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
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Results are estimates for informational purposes and are not financial, medical or legal advice.