Gradians to Degrees Converter
Quick answer: To convert gradians to degrees, multiply by 0.9. For example, 10 grad is 9 °. One gradian equals 0.9 °.
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Use the Gradians to Degrees Converter
Gradians to Degrees formula and what each symbol means
° = grad × 0.9
| Symbol | Meaning |
|---|---|
| grad | Gradian |
| ° | Degree |
Gradians to Degrees examples
1 grad
1 grad × 0.9 = 0.9 °.
10 grad
10 grad × 0.9 = 9 °.
100 grad
100 grad × 0.9 = 90 °.
Gradians compared with Degrees
One ° is 1.111 times as large as one grad, so your number gets smaller when you convert gradians to degrees and bigger when you convert back. If the answer is not smaller than what you typed, you multiplied instead of dividing.
About gradians and degrees
Gradian (grad): 1/400 of a full turn, also called a gon. Degree (°): 1/360 of a full turn.
Where gradians to degrees conversions are used
Trigonometry functions in most programming languages expect radians. Navigation and surveying use degrees, while maths, physics and programming use radians.
How to calculate Gradians to Degrees step by step
- Enter the value in grad (the starting unit).
- Multiply by 0.9, because 1 grad = 0.9 °.
- The product is the value in °. To go back, divide by 0.9 or multiply by 1.111111.
Popular angle conversions
How to read your Gradians to Degrees result
A full turn is 360 degrees, 400 gradians or 2π radians (about 6.28319).
| GRADIANS | DEGREES |
|---|---|
| 1 | 0.9 |
| 2 | 1.8 |
| 5 | 4.5 |
| 10 | 9 |
| 20 | 18 |
| 50 | 45 |
| 100 | 90 |
| 1,000 | 900 |
Degrees to Gradians: quick table
| DEGREES | GRADIANS |
|---|---|
| 1 | 1.111111 |
| 5 | 5.555556 |
| 10 | 11.11111 |
| 25 | 27.77778 |
| 50 | 55.55556 |
| 100 | 111.1111 |
| 250 | 277.7778 |
| 500 | 555.5556 |
Common mistakes when calculating Gradians to Degrees
- Mixing gradians (400 per turn) with degrees (360 per turn).
- Dividing when you should multiply: from grad to ° multiply by 0.9; from ° to grad divide by 0.9.
Gradians to Degrees FAQ
How many ° are in 1 grad?
1 grad equals 0.9 °.
How many grad are in 1 °?
1 ° equals 1.111111 grad.
Is 1 grad = 0.9 ° an exact conversion?
The factor is shown rounded to 7 significant figures (0.9). The calculator above uses more digits.
What is a gradian (grad)?
1/400 of a full turn, also called a gon.
How can I estimate gradians to degrees in my head?
One ° is 1.111 times as large as one grad, so your number gets smaller when you convert gradians to degrees and bigger when you convert back. If the answer is not smaller than what you typed, you multiplied instead of dividing.
What is 500 grad in degrees?
500 grad = 450 ° (since 500 × 0.9).
What is 15 grad in degrees?
15 grad = 13.5 ° (since 15 × 0.9).
What is 75 grad in degrees?
75 grad = 67.5 ° (since 75 × 0.9).
How many decimals should I keep when converting grad to °?
Match the precision of your original measurement. For example, 9 ° rounds to 9 ° at 3 significant figures; keep more digits only for engineering or scientific work.
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Method, review and disclaimer
Edited by: Hemant Kumar and Anjita Rai, founders of ToolsVault (SEO and content professional, not a licensed adviser). Method: this tool runs in your browser using the formula shown on this page; the numbers you enter are not sent to our servers. Sources: NIST SP 811, Appendix B.8: conversion factors, BIPM: the SI derived units