1. How to convert degrees to gradians
The conversion is a single multiplication: grad = ° × 1.11111111111. Both units are defined
against the same base — the radian (rad) — so the factor is fixed and the result
is exact to the precision shown.
Worked at the two values people ask for most: 1 ° = 1.1111111 grad and
45 ° = 50 grad. Going the other way, ° = grad × 0.9, so
1 grad = 0.9 °.
Results are given to eight significant figures. That is more precision than most jobs need — for a rough figure, treat 1 ° as about 1.1111111 grad and adjust — but rounding early and multiplying afterwards is how a small error becomes a visible one, so the full figure is what the converter carries.
2. Degrees to Gradians conversion table
| Degrees (°) | Gradians (grad) |
|---|---|
| 1 ° | 1.1111111 grad |
| 15 ° | 16.666667 grad |
| 30 ° | 33.333333 grad |
| 45 ° | 50 grad |
| 60 ° | 66.666667 grad |
| 90 ° | 100 grad |
| 120 ° | 133.33333 grad |
| 180 ° | 200 grad |
| 270 ° | 300 grad |
| 360 ° | 400 grad |
Every row is the same factor applied — nothing in the table is a special case, and any value in between behaves the same way. Type your own figure into the converter above and the Formula tile shows the arithmetic being used, so the result is checkable rather than taken on trust.
3. What the two units are
- Degrees (°). One ° is 0.017453293 rad.
- Gradians (grad). One grad is 0.015707963 rad.
Both are converted through the radian (rad): the value is multiplied by its own unit's factor to reach the base, then divided by the target unit's factor to leave it. No direct degrees to gradians factor has to exist or be kept correct, which is also why the converter can show the same value in all 7 angle units at once.
A radian is the angle subtending an arc equal to the radius, so a full turn is 2π radians and one radian is about 57.2958°. Gradians divide the right angle into 100 rather than 90, which is why 90° is 100 grad — a surveying convention that never displaced degrees.
If the pair you actually want is not this one, the full unit converter runs every 7 angle units off the same factor table, along with 11 other categories of measurement.
4. Degrees to Gradians FAQs
How do I convert degrees to gradians?
Multiply by 1.11111111111. 1 ° = 1.1111111 grad, and 45 ° = 50 grad. The factor is exact to the precision shown, so the only rounding is the one you choose to do at the end.
How many gradians is 1 °?
1 ° = 1.1111111 grad. The full formula is grad = ° × 1.11111111111, and 1 grad = 0.9 ° going the other way.
What is 45 ° in grad?
45 ° = 50 grad. The table above works the same factor through 10 values, and the converter takes any figure you type — including decimals.
How do I convert grad to °?
° = grad × 0.9, so 1 grad = 0.9 °. Use the Swap button in the converter to reverse the direction without retyping the value.
How many degrees in a radian?
About 57.2958°, since a full turn is 2π radians. A radian is the angle that subtends an arc equal to the circle’s radius, which is why it is the natural unit for trigonometry and calculus rather than an arbitrary division of the circle.
Is anything I type sent to a server?
No. The factor table ships with the page and every conversion runs in your browser. Nothing is uploaded, logged or written to storage, and the converter keeps working offline once the page has loaded.