Degrees to Gradians Converter
Quick answer: To convert degrees to gradians, multiply by 1.111111. For example, 10 ° is 11.11111 grad. One degree equals 1.111111 grad.
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Use the Degrees to Gradians Converter
Degrees to Gradians formula and what each symbol means
grad = ° × 1.111111
| Symbol | Meaning |
|---|---|
| ° | Degree |
| grad | Gradian |
Degrees to Gradians examples
1 °
1 ° × 1.111111 = 1.111111 grad.
10 °
10 ° × 1.111111 = 11.11111 grad.
100 °
100 ° × 1.111111 = 111.1111 grad.
Degrees compared with Gradians
One ° is 1.111 times as large as one grad, so your number gets bigger when you convert degrees to gradians and smaller when you convert back. If the answer is not larger than what you typed, you divided instead of multiplying.
About degrees and gradians
Degree (°): 1/360 of a full turn. Gradian (grad): 1/400 of a full turn, also called a gon.
Where degrees to gradians 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 Degrees to Gradians step by step
- Enter the value in ° (the starting unit).
- Multiply by 1.111111, because 1 ° = 1.111111 grad.
- The product is the value in grad. To go back, divide by 1.111111 or multiply by 0.9.
Popular angle conversions
How to read your Degrees to Gradians result
Quick estimate: multiply by about 1.1 to get gradians from degrees; this is within 1.0% of the exact factor. A full turn is 360 degrees, 400 gradians or 2π radians (about 6.28319).
| DEGREES | GRADIANS |
|---|---|
| 1 | 1.111111 |
| 2 | 2.222222 |
| 5 | 5.555556 |
| 10 | 11.11111 |
| 20 | 22.22222 |
| 50 | 55.55556 |
| 100 | 111.1111 |
| 1,000 | 1,111.111 |
Gradians to Degrees: quick table
| GRADIANS | DEGREES |
|---|---|
| 1 | 0.9 |
| 5 | 4.5 |
| 10 | 9 |
| 25 | 22.5 |
| 50 | 45 |
| 100 | 90 |
| 250 | 225 |
| 500 | 450 |
Common mistakes when calculating Degrees to Gradians
- Mixing gradians (400 per turn) with degrees (360 per turn).
- Dividing when you should multiply: from ° to grad multiply by 1.111111; from grad to ° divide by 1.111111.
Degrees to Gradians FAQ
How many grad are in 1 °?
1 ° equals 1.111111 grad.
How many ° are in 1 grad?
1 grad equals 0.9 °.
Is 1 ° = 1.111111 grad an exact conversion?
The factor is shown rounded to 7 significant figures (1.111111). The calculator above uses more digits.
What is a degree (°)?
1/360 of a full turn.
How can I estimate degrees to gradians in my head?
Quick estimate: multiply by about 1.1 to get gradians from degrees; this is within 1.0% of the exact factor.
What is 150 ° in gradians?
150 ° = 166.6667 grad (since 150 × 1.111111).
What is 0.5 ° in gradians?
0.5 ° = 0.5555556 grad (since 0.5 × 1.111111).
What is 25 ° in gradians?
25 ° = 27.77778 grad (since 25 × 1.111111).
How many decimals should I keep when converting ° to grad?
Match the precision of your original measurement. For example, 11.11111 grad rounds to 11.1 grad at 3 significant figures; keep more digits only for engineering or scientific work.
More in Angle converters
- Gradians to Radians Converter
- Revolutions to Degrees Converter
- Gradians to Revolutions Converter
- Radians to Revolutions Converter
- Radians to Degrees Converter
- Radians to Gradians Converter
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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