Authoritative definitions of the International System of Units and SI prefixes.
Dedicated unit pair
Gradians to Radians
Convert gon to rad instantly, then review the formula, assumptions, and rounding guidance.
AngleInstant result
Decimals
Formula result = input × 0.015707963267948967 ÷ 1. 1 gon = 0.0157 rad
Common examples
One value, several units
Radians0.0157 rad
Degrees0.9 °
Turns0.0025 turn
Arcminutes54 ′
Arcseconds3,240 ″
Conversion table
| gon | rad |
|---|---|
| 1 gon | 0.0157 rad |
| 2 gon | 0.0314 rad |
| 5 gon | 0.0785 rad |
| 10 gon | 0.1571 rad |
| 25 gon | 0.3927 rad |
| 50 gon | 0.7854 rad |
| 100 gon | 1.5708 rad |
Conversion chart
1 gon0.0157 rad
5 gon0.0785 rad
10 gon0.1571 rad
25 gon0.3927 rad
50 gon0.7854 rad
Worked example
A full turn is 360 degrees or 2π radians.
Unit definition
Gradians (gon) One gradians equals 0.0157079632679 radian.
Unit history
Gradians is represented here using its modern SI definition or an internationally accepted relationship to an SI base unit.
Step by step
1. Parse the value, including fractions.
2. Convert gon to radian.
3. Convert the base value to rad and apply your display precision.
Understand the result before using it
Gradians to Radians converts a value measured in Gradians (gon) into the equivalent value in Radians (rad). The numerical value changes because the size and definition of the selected unit changes; the underlying quantity does not.
Calculated result
The conversion follows the displayed unit relationship. Display rounding can hide additional digits, and measured inputs cannot become more accurate merely by changing units.
Formula, assumptions, and example
Formula
result = input × 0.015707963267948967 ÷ 1
Assumptions
- Gradians and Radians represent the same angle quantity.
- The input is expressed in gon; the output is expressed in rad.
- The unit definitions and conventional relationship shown on this page apply.
Worked example
1 gon = 0.0157079632679 rad. For another value, apply the same relationship and round only to the precision your source measurement supports.
When to use it
Good uses
- Read a gon measurement in a document that expects rad.
- Compare a gradians value with a value reported in radians.
- Check the gon-to-rad arithmetic before copying the result into another calculation.
Limitations
Common mistakes to avoid
- Do not confuse gon with another unit that has a similar name or symbol.
- Round the output to a precision justified by the original measurement.
- Verify safety-critical, regulated, laboratory, and contractual conversions against the controlling standard.
Sources and further reading
These references explain the underlying standards or provide authoritative context. Your own contract, institution, clinician, product documentation, local code, or governing standard may be the controlling source.
Guidance on unit names, symbols, conversions, and numerical presentation.
Questions about this calculation
How do I convert Gradians to Radians?
result = input × 0.015707963267948967 ÷ 1 Using the displayed relationship, 1 gon equals 0.0157079632679 rad.
How many Radians are in one Gradians?
One Gradians is 0.0157079632679 Radians. The displayed digits may be rounded.
Can I reverse the gon to rad conversion?
Yes. Swap the source and target units in the converter. The reverse relationship converts rad back to gon.
Is the Gradians to Radians result exact?
The conversion follows the displayed unit relationship. Display rounding can hide additional digits, and measured inputs cannot become more accurate merely by changing units.