grad to rad Converter

Convert Gradian to Radian instantly.

Free online converter with accurate results and clear explanations.

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Default example shown while the interactive calculator loads.

How This Tool Works

Gradians and radians use different full-circle scales. A full circle is 400 grad or 2π radians, so 1 grad equals π / 200 radians.

To convert gradians to radians, multiply the gradian value by π / 200. For example, 100 grad × π / 200 = π / 2 radians.

To convert radians back to gradians, multiply the radian value by 200 / π.

Why This Matters

Radians are the standard angle unit for trigonometry, calculus, physics, and many programming APIs. Converting gradians to radians keeps angle measurements compatible with formulas that expect radian input.

  • Math and physics: Use radians for arc length, angular velocity, and trigonometric formulas.
  • Programming: Most trigonometric functions expect radians, not gradians or degrees.
  • Surveying and engineering: Convert gradian measurements before using radian-based analysis tools.

Common Mistakes to Avoid

  • Use the full-circle ratio: 400 grad equals 2π radians.
  • Do not use π / 2 per grad: π / 2 radians equals 100 grad, not 1 grad.
  • Check benchmark values: 100 grad should equal π / 2 radians, and 400 grad should equal 2π radians.

Tips for Best Results

Use exact π notation when precision matters, then round only the final decimal result.

Good checkpoints are 100 grad = π / 2 rad, 200 grad = π rad, and 400 grad = 2π rad.

Frequently Asked Questions

Common questions about the grad to rad Converter

Enter your Gradian value in the input field, and the converter will automatically calculate the equivalent Radian value. You can also click the swap button to reverse the conversion direction.
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Sources & References

International System of Units (SI): plane angle

Plane angle is measured in the radian (rad); 1° = π/180 rad. Conversions between SI and other units use exact, internationally agreed factors maintained by NIST.
→Source: NIST — International System of Units (SI)

International System of Units (SI)

Authoritative definitions for plane angle, from the BIPM SI Brochure (9th edition), the defining reference for the SI.
→Source: BIPM — SI Brochure (9th ed.)

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