Radians To Grads Converter

radian to grad – How to convert rad to grad

Radians and grads might not show up in casual conversation, but in engineering, surveying, and mathematics, they play a central role in how angles are calculated and applied. If you're working with circular motion, coordinate geometry, or land measurement, you may need to convert radians to grads to match standards or specifications.

Here’s what each unit means, how they relate to each other, and how to convert between them.

What is a radian (rad)?

A radian is the standard angle unit in mathematics and physics. Defined as the angle created when the arc length equals the radius of a circle, it’s a natural unit in trigonometry and calculus.

• 1 full circle = 2π radians

• 1 rad ≈ 57.2958 degrees

Radians don’t depend on arbitrary divisions—they arise from the geometry of the circle itself. That’s why they’re favored in formulas involving rotation, harmonic motion, and wave functions.

What is a grad (gon)?

A grad (also called gon) divides a full circle into 400 equal parts. Unlike degrees (360 per circle), grads offer a decimal-friendly way to split angles.

• 100 grads = right angle

• 200 grads = straight angle

• 400 grads = full rotation

The gradian system was introduced during the French metrication reforms in the 18th century to make calculations in surveying and engineering more aligned with base-10 systems.

It remains in use across Europe in civil engineering, mapping, and geodetic tools, particularly when decimal precision is preferred.

How to convert radian to grad

We know that:

• 2π radians = 400 grads

To convert, isolate 1 radian:

1 rad = 400 ÷ (2π)
1 rad ≈ 63.662 grads

Formula

grad = radian × (200 / π)

You can also remember it as:

grad ≈ radian × 63.662

This gives a direct, decimal-based conversion.

Example: Convert 1.5 radians to grads

grad = 1.5 × (200 / π)
grad ≈ 1.5 × 63.662
grad ≈ 95.49

So, 1.5 radians is approximately 95.49 grads.

To speed things up, try the Angle Converter for quick, precise results. Want more conversions? Explore the full range of Conversion tools.

Did you know?

• Grads were part of the French Revolution’s push to decimalize all measurements, including time, weight, and angles.

• Some European theodolites and leveling tools default to grads for ease of calculation in the field.

• Radians simplify math formulas in physics and calculus because they’re unitless in many equations.

• Grads are ideal for slope calculations, especially in civil and railway engineering, where decimal-based geometry is preferred.

• In map projection systems, particularly in some European countries, angle data is still stored and processed in grads.

When mapping meets math: grads in surveying

In land surveying, accuracy is essential—and calculations often need to be made quickly on-site. That’s one of the main reasons grads became popular in geodetic work, especially in continental Europe.

A right angle being 100 grads makes it easy to express slopes, directions, and divisions in clean decimals. In contrast, radians are favored in backend math—used in software to calculate rotations and angles internally.

For example, a GIS (Geographic Information System) might let engineers input angles in grads for simplicity, while the underlying math engine handles those angles in radians. This balance of user-friendly grads and formula-friendly radians makes the radian-to-grad conversion a crucial one in geospatial technology.

From pure math to practical fieldwork

Radians and grads come from very different worlds—one from the clean geometry of circles, the other from the decimal-focused needs of engineering. But converting between them bridges mathematics and measurement, helping align calculations with real-world tools and systems.

Remember the formula:

grad = radian × (200 / π)
or
grad ≈ radian × 63.662

For more conversions across angle systems, visit the Angle Converter or browse dozens of other categories with the full Conversion tools collection.