Convert Gradians (grad) to Radians (rad)

1 gradian equals 0.015708 radians.

Formula: rad = grad × 0.015708

Gradian to Radian Converter

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How to Convert Gradian to Radian

1 gradian = 0.015708 radians exact

Radian = Gradian × 0.015708

Example: 1 grad × 0.015708 = 0.015708 rad

Reverse Conversion

To convert radians back to gradians:

  • Remember, 1 radian equals 63.662 gradians.
  • To convert 0.015708 rad to grad, multiply 0.015708 x 63.662, resulting in 1 grad.

exact This conversion factor is exact by international definition.

Common Gradian to Radian Conversions

Gradian to Radian (Part 1)
Gradian Radian Actions
1 gradian 0.015708 radians
5 gradians 0.0785398 radians
10 gradians 0.15708 radians
25 gradians 0.392699 radians
Gradian to Radian (Part 2)
Gradian Radian Actions
50 gradians 0.785398 radians
100 gradians 1.5708 radians
500 gradians 7.85398 radians
1000 gradians 15.708 radians

Gradians to radians Conversion Table

Reference table with common gradians to radians conversions. All values calculated with high precision.

Gradians to Radians Table
0.01 to 50

Gradians Radians Actions
0.01 grad 0.00015708 rad
0.025 grad 0.000392699 rad
0.05 grad 0.000785398 rad
0.1 grad 0.0015708 rad
14 grad 0.00392699 rad
12 grad 0.00785398 rad
1 grad 0.015708 rad
2 12 grad 0.0392699 rad
5 grad 0.0785398 rad
10 grad 0.15708 rad
25 grad 0.392699 rad
50 grad 0.785398 rad

Gradians to Radians Table
100 to 10000000

Gradians Radians Actions
100 grad 1.5708 rad
250 grad 3.92699 rad
500 grad 7.85398 rad
1000 grad 15.708 rad
2500 grad 39.2699 rad
5000 grad 78.5398 rad
10000 grad 157.08 rad
25000 grad 392.699 rad
50000 grad 785.398 rad
100000 grad 1570.8 rad
250000 grad 3926.99 rad
500000 grad 7853.98 rad
1000000 grad 15708 rad
2500000 grad 39269.9 rad
5000000 grad 78539.8 rad
10000000 grad 157080 rad

Radians to Gradians Table
0.0001 to 12

Radians Gradians Actions
0.0001 rad 0.0063662 grad
0.00025 rad 0.0159155 grad
0.0005 rad 0.031831 grad
0.001 rad 0.063662 grad
0.0025 rad 0.159155 grad
0.005 rad 0.31831 grad
0.01 rad 0.63662 grad
0.025 rad 1.59155 grad
0.05 rad 3.1831 grad
0.1 rad 6.3662 grad
14 rad 15.9155 grad
12 rad 31.831 grad

Radians to Gradians Table
1 to 100000

Radians Gradians Actions
1 rad 63.662 grad
2 12 rad 159.155 grad
5 rad 318.31 grad
10 rad 636.62 grad
25 rad 1591.55 grad
50 rad 3183.1 grad
100 rad 6366.2 grad
250 rad 15915.5 grad
500 rad 31831 grad
1000 rad 63662 grad
2500 rad 159155 grad
5000 rad 318310 grad
10000 rad 636620 grad
25000 rad 1591550 grad
50000 rad 3183100 grad
100000 rad 6366200 grad

Definition of Gradian

Definition

The gradian (grad) divides a right angle into 100 equal parts, making 400 gradians in a full circle.

It is used in surveying, geodesy, cartography, and some engineering standards, especially in parts of Europe.

Exact factor
1 grad = π/200 rad (exact)
Examples
  • 100 grad = 90°
  • 200 grad = 180°

Definition of Radian

Definition

The radian (rad) is the SI derived unit of plane angle. It is defined as the angle subtended at the center of a circle by an arc equal in length to the radius.

Although mathematically dimensionless, the radian is retained as a named unit in the SI to preserve clarity in scientific, engineering, physics, trigonometry, and calculus contexts.

Exact factor
Base unit: 1 rad = 1 rad; full circle: 2π rad = 360°
Examples
  • π rad = 180°
  • 1 rad ≈ 57.2958°
  • 2π rad = 1 turn

About the Gradian

Facts & Uses

  • 1 gradian (grad, gon) = 1/400 of a full circle = 0.9° exactly. Designed to give a right angle a clean round value of 100 grad.
  • Standard in European surveying (especially France, Germany, and parts of Eastern Europe), civil engineering, and topographic mapping.
  • Used in some scientific calculators as an alternative angle mode (DEG / RAD / GRAD), though rarely encountered in everyday math.
  • Convenient for decimal calculations in surveying because percentages of a quadrant map directly: 50 grad = 45° = half a right angle.

Curiosities

  • The gradian was introduced during the French Revolution (1790s) as part of the metric system's push for decimalization — even time was briefly decimalized too.
  • The name "gon" (from Greek "gōnía", angle) is the official ISO 31-1 name; "gradian" and "grade" are common synonyms.
  • Surveyors who use the gradian point out that a 1% slope = 0.6366 grad — but they prefer the cleaner 1° = 1.111 grad relationship for plan reading.
  • Approximate equivalents: 1 grad = 0.9° = π/200 rad ≈ 0.01571 rad; 100 grad = 90° = π/2 rad.

Sources

About the Radian

Facts & Uses

  • SI coherent unit of plane angle: 1 rad = the angle subtended at a circle's center by an arc equal in length to the radius. 1 full circle = 2π rad ≈ 6.283 rad.
  • Universal in mathematics, physics, engineering, and computer graphics — wherever calculus or trigonometric derivatives are involved.
  • Standard for angular velocity (rad/s), angular acceleration (rad/s²), and phase angles in electrical engineering and signal processing.
  • Common reference: π/6 rad = 30°, π/4 = 45°, π/3 = 60°, π/2 = 90°, π = 180°, 2π = 360°.

Curiosities

  • The radian was first proposed by Roger Cotes in 1714, but the name "radian" wasn't coined until 1873 by James Thomson (brother of Lord Kelvin).
  • Programming functions like Math.sin() and Math.cos() in JavaScript, Python, C, and most languages take radians as input — a frequent source of bugs for developers expecting degrees.
  • The reason calculus prefers radians: the derivative of sin(x) is cos(x) only when x is in radians. With degrees, you'd need a π/180 factor everywhere.
  • Approximate equivalents: 1 rad ≈ 57.2958° ≈ 63.66 grad ≈ 3437.75 arcminutes.

Sources

Frequently Asked Questions

How many radians are in one gradian?

One gradian equals 0.015708 radians. To convert, multiply the gradian value by 0.015708. For the reverse, divide the radian value by 0.015708 (or multiply by 63.662).

What is 103.3 gradians in radians?

103.3 gradians = 1.6226 radians. This is one of the most commonly searched conversions for this pair.

How precise is the gradian-to-radian conversion?

The factor 0.015708 is accurate to 6 significant figures, derived from international measurement standards. Our calculator uses full precision internally.

Looking for the reverse? Convert Radian to Gradian

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Conversion factors verified against BIPM, ISO 80000-3 1 turn = 2π rad = 360° (exact, ISO 80000-3). Last reviewed: March 2026
Adilson Fernandes By Adilson Fernandes
Tiago Fernandes Reviewed by Tiago Fernandes

All unit conversions on CoolConversion use conversion factors defined or documented by internationally recognised standards bodies (such as ISO and NIST), including both SI and non-SI units.

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