In 1 gradians there are 0.015708 radians. Meanwhile in 1 radians there are 63.661977 gradians. Keep reading to learn more about each unit of measure and how they are calculated. Or just use the Radians to Gradians calculator above to convert any number.
* Values rounded to 6 decimal places for readability
To convert gradians to radians, use the fact that a full turn is 400 gradians and 2π radians. That sets the conversion ratio.
Formula (grad to rad):
Why it works:
Quick examples:
For a decimal value, multiply your gradian number by π/200, then round as needed. This method gives an exact gradians to radians conversion every time.
A gradian, also called a gon, is a unit for measuring angles. A full circle equals 400 gradians. This system is often used in surveying, mapping, and some engineering work.
A radian is the standard unit of angle in math and science. A full circle equals (2\pi) radians. Radians tie angles to circles and arc length, which makes them useful in formulas.
Use this formula:
[ \text{radians}=\text{gradians}\times\frac{\pi}{200} ]
This works because 200 gradians equals (\pi) radians.
The conversion factor is:
[ 1\ \text{grad}=\frac{\pi}{200}\ \text{rad}\approx 0.015707963\ \text{rad} ]
Multiply gradians by (\pi/200) to get radians.
Since 200 gradians equals (\pi) radians, 100 gradians is half of that:
[ 100\ \text{grad}=\frac{\pi}{2}\ \text{rad}\approx 1.57079633\ \text{rad} ]
(\pi) radians equals half a circle, which is 200 gradians:
[ \pi\ \text{rad}=200\ \text{grad} ]
Here are a few quick conversions:
A full circle is 400 gradians and (2\pi) radians. Half a circle is 200 gradians and (\pi) radians. That link sets the scale, so gradians convert to radians using (\pi/200).
They all measure angles, but they split a circle in different ways:
Gradians make right angles clean (a right angle is 100 gradians). Radians fit well in trig and calculus.
Use the reverse formula:
[ \text{gradians}=\text{radians}\times\frac{200}{\pi} ]
This turns radian values into the 0 to 400 gradian scale.
Round based on your use case. For most homework and basic work, 4 to 6 decimal places is enough. For surveying and engineering, keep more digits until the final step to reduce rounding error.
Yes. Angles can go past one full turn. For example:
[ 500\ \text{grad}=500\times\frac{\pi}{200}=\frac{5\pi}{2}\ \text{rad} ]
That equals one full turn plus an extra quarter turn.
Yes. Both can measure angles in either direction. Positive angles usually go counterclockwise, and negative angles go clockwise, unless a field uses a different sign rule.
The Calculate Box tool to convert gradians to radians uses the open source script Convert.js to convert units of measurement. To use this tool, simply type a gradians value in the box and have it instantly converted to radians.