Convert Gradians (grad) to Degrees (°)

Q: How many degrees are in one gradian?

Exactly 0.9 degrees. The ratio 360°/400 grad = 9/10 is exact by definition. The inverse: 1° = 10/9 grad ≈ 1.1111 grad.

Q: Which countries still use gradians?

France, Germany, Switzerland, Belgium, Sweden, and other European countries use gradians in professional surveying. European theodolites default to grad mode. Degrees dominate everyday use, but surveyors and civil engineers work daily with gradians.

1 gradian equals 0.9 degrees.

Formula: ° = grad × 0.9

Gradian to Degree Converter

What Is a Gradian?

The gradian (grad), also called gon or grade, divides a right angle into exactly 100 equal parts, making a full circle equal to 400 gradians. Its exact relationship to the radian is 1 grad = π/200 rad.

Introduced during the French Revolution (1790s) as part of the metric reform, the gradian was designed to decimalize angle measurement. While it never replaced degrees globally, it remains the standard angular unit in continental European surveying, geodesy, and cadastral systems — especially in France, Belgium, Germany, and Scandinavia.

Key equivalences: 100 grad = 90°; 200 grad = 180°; 400 grad = 360°.

What Is a Degree?

The degree (°) is a non-SI unit of plane angle defined as exactly 1/360 of a full rotation. It is accepted for use with the SI due to its importance in navigation, surveying, engineering, and astronomy.

The 360-degree circle originates from ancient Babylonian astronomy and remains the dominant angular unit worldwide — used in compasses, protractors, GPS coordinates, and virtually every consumer application involving angles.

Key equivalences: 1° = π/180 rad = 60′ = 3,600″ = 10/9 grad.

Gradians to Degrees Formula

The conversion factor is exact:

degrees = gradians × 9/10 exact

This comes from the ratio: 360° / 400 grad = 9/10 = 0.9. So 1 gradian = exactly 0.9 degrees.

Worked Example

Convert a European survey bearing of 150 grad to degrees:

Multiply: 150 × 0.9 = 135°

So 150 gradians = exactly 135°. Multiples of 10 grad always convert to clean degree values ending in whole or half degrees.

Quick Estimation

For mental math, subtract 10% from the gradian value. Example: 250 grad − 10% = 250 − 25 = 225° (exact: 225°). This works perfectly because the factor is exactly 0.9.

Common Conversions at a Glance

Gradians	Degrees
1 grad	0.9°
50 grad	45°
100 grad (right angle)	90°
150 grad	135°
200 grad (straight)	180°
300 grad	270°
400 grad (full circle)	360°

Which Is Bigger: Gradian or Degree?

A degree is 1.11 times larger than a gradian — or equivalently, a gradian is 90% of a degree. These are the most similar-sized angular units across the two systems. The difference is subtle: 100 grad vs 90° for a right angle — the gradian is simply a slightly finer subdivision.

When You Need This Conversion

Importing European survey data: Theodolite readings and total station exports from France, Germany, or Scandinavia use gradians. Converting to degrees is needed for GIS software that defaults to degrees or for international collaboration.
CAD interoperability: Some European CAD systems use centesimal angles (gradians). Importing files into degree-based systems (AutoCAD, SolidWorks) requires conversion.
Scientific calculator mode: Calculators in GRAD mode display results in gradians. Converting to DEG mode for reporting or further calculations is a daily task for European surveyors.
French cadastral records: Property boundary angles in the French land registry are recorded in gradians. Real estate transactions involving French properties require conversion to degrees for international documentation.

Frequently Asked Questions

How many degrees are in one gradian?

Exactly 0.9 degrees. The ratio 360°/400 grad = 9/10 is exact by definition. The inverse: 1° = 10/9 grad ≈ 1.1111 grad.

What is the difference between gradians, gons, and grades?

They are different names for the same unit. "Gradian" is the ISO standard name, "gon" is used in German (DIN) and Scandinavian standards, "grade" is the French term. All mean 1/400 of a circle. Calculators label it "GRA", "GRAD", or "G".

Why were gradians invented?

Created during the French Revolution (1790s) to decimalize angles — 100 grad per right angle makes percentages and mental math simpler than 90°. A half right angle is 50 grad (not 45°), a tenth is 10 grad (not 9°).

Which countries still use gradians?

France, Germany, Switzerland, Belgium, Sweden, and other European countries use gradians in professional surveying. European theodolites default to grad mode. Degrees dominate everyday use, but surveyors and civil engineers work daily with gradians.

What is the relationship between gradians and slope percentage?

For small angles, 1 grad ≈ 1.57% slope (since tan(1 grad) ≈ 0.01571). This near-linear relationship is why gradians are preferred in road and railway design — slope percentages map almost directly to gradian values.

Common Gradian to Degree Conversions

Gradian to Degree (Part 1)

Gradian	Degree	Actions
0 gradians	0 degrees
50 gradians	45 degrees
100 gradians	90 degrees

Gradian to Degree (Part 2)

Gradian	Degree	Actions
200 gradians	180 degrees
400 gradians	360 degrees

Gradians to degrees Conversion Table

Reference table with common gradians to degrees conversions. All values calculated with high precision.

Gradians to Degrees Table
0.001 to 5

Gradians	Degrees	Actions
0.001 grad	0.0009 °
0.0025 grad	0.00225 °
0.005 grad	0.0045 °
0.01 grad	0.009 °
0.025 grad	0.0225 °
0.05 grad	0.045 °
0.1 grad	0.09 °
14 grad	0.225 °
12 grad	0.45 °
1 grad	0.9 °
2 12 grad	2 14 °
5 grad	4 12 °

Gradians to Degrees Table
10 to 1000000

Gradians	Degrees	Actions
10 grad	9 °
25 grad	22.5 °
50 grad	45 °
100 grad	90 °
250 grad	225 °
500 grad	450 °
1000 grad	900 °
2500 grad	2250 °
5000 grad	4500 °
10000 grad	9000 °
25000 grad	22500 °
50000 grad	45000 °
100000 grad	90000 °
250000 grad	225000 °
500000 grad	450000 °
1000000 grad	900000 °

Degrees to Gradians Table
0.0001 to 12

Degrees	Gradians	Actions
0.0001 °	0.000111111 grad
0.00025 °	0.000277778 grad
0.0005 °	0.000555556 grad
0.001 °	0.00111111 grad
0.0025 °	0.00277778 grad
0.005 °	0.00555556 grad
0.01 °	0.0111111 grad
0.025 °	0.0277778 grad
0.05 °	0.0555556 grad
0.1 °	0.111111 grad
14 °	0.277778 grad
12 °	0.555556 grad

Degrees to Gradians Table
1 to 100000

Degrees	Gradians	Actions
1 °	1.11111 grad
2 12 °	2.77778 grad
5 °	5.55556 grad
10 °	11.1111 grad
25 °	27.7778 grad
50 °	55.5556 grad
100 °	111.111 grad
250 °	277.778 grad
500 °	555.556 grad
1000 °	1111.11 grad
2500 °	2777.78 grad
5000 °	5555.56 grad
10000 °	11111.1 grad
25000 °	27777.8 grad
50000 °	55555.6 grad
100000 °	111111 grad

Looking for the reverse? Convert Degree to Gradian

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Conversion factors verified against BIPM, ISO 80000-3 1 turn = 2π rad = 360° (exact, ISO 80000-3). Last reviewed: March 2026

By Adilson Fernandes

Reviewed by Tiago Fernandes

All unit conversions on CoolConversion use conversion factors defined or documented by internationally recognised standards bodies (such as ISO and NIST), including both SI and non-SI units.