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degree to grad – How to convert ° to grad
If you’ve only worked with angles in degrees, the term “grad” (also known as gon) might seem a bit obscure. But grads are still very much in use today, especially in surveying, engineering, and mapping—fields where precision and decimal-friendly calculations matter. Converting between degrees and grads is easier than you think, and in many cases, it’s essential.
Let’s break down what each unit means, how to convert between them, and where grads show up in the real world.
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What is a degree (°)?
A degree is the most familiar unit for measuring angles. A full circle is made up of 360 degrees, which makes it convenient for dividing into equal parts—90° for right angles, 180° for straight lines, and so on.
The origin of this system goes back thousands of years to the Babylonians, who used base-60 math. Despite its ancient roots, the degree is still everywhere today—from your geometry homework to your smartphone’s compass to the axis of satellite dishes.
What is a grad (gon)?
A grad, or gon, splits a circle into 400 equal parts. That means:
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100 grads = 1 right angle
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200 grads = a straight line
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400 grads = a full circle
Grads were introduced during the French metrication movement in the late 18th century. The idea was to make everything decimal-based, which made calculations cleaner—especially for tasks like land surveying, where angles are often added and subtracted quickly on-site.
While not as globally widespread as degrees or radians, grads are still used in continental Europe, especially in civil engineering and with digital instruments like theodolites and total stations.
How to convert degree to grad
The relationship between degrees and grads is simple. Since:
360 degrees = 400 grads
we can set up a direct ratio.
✅ Formula
grad = degree × (10 / 9)
This equation takes any angle in degrees and converts it to grads with just one multiplication.
✅ Example: Convert 45 degrees to grads
grad = 45 × (10 / 9)
grad = 450 / 9
grad = 50
So, 45 degrees equals 50 grads.
Want to convert more angles on the fly? Try the Angle Converter or check out all the available options in our Conversion tools.
Did you know?
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The gradian system was part of a revolutionary push in 18th-century France to decimalize all measurements—time, distance, weight, and even angles.
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Grads simplify surveying math because one right angle equals 100 grads. It’s easier to add or subtract without fractions or decimals.
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Geodetic instruments in Europe often default to grads, especially when dealing with national mapping grids.
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Digital calculators—like those made by Casio and HP—often include a “grad” mode alongside degrees and radians.
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In civil engineering blueprints, grads are still occasionally used to specify exact slopes or curve geometry.
Revolutionary math: how grads came to be
During the French Revolution, reformers wanted to scrap old systems and build a new world based on rationality and decimal math. That ambition extended to how circles were measured. Instead of the old Babylonian 360-degree circle, the new system proposed 400 units—grads—to align with the rest of the metric system.
One right angle would now be a clean 100 grads, and each grad could be broken into 100 centigrads. In theory, this made calculations faster, especially for land division and mapping.
The system never caught on globally, but surveyors, engineers, and European mapping agencies still use grads today—especially when precision and decimal compatibility are a priority.
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Where grads make your life easier
You might not use grads every day, but in certain jobs and regions, they’re everywhere. If you’re working with digital surveying equipment, referencing topographic maps, or collaborating on European infrastructure projects, grads are the preferred unit.
Now you’ve got the formula:
grad = degree × (10 / 9)
And whether you’re running calculations manually or looking for a faster way to get results, you can always jump into the Angle Converter or browse more tools with the Conversion tools page.
