How to convert 180 degrees to 3.14159 radians?

180 degrees = π radians (half circle)

How to convert 1 radian to 57.3 degrees?

1 radian = 57.3 degrees (approximately)

How to convert 90 degrees to 100 gradians?

90 degrees = 100 gradians (right angle)

How do I convert degrees to radians?

Multiply degrees by π/180. So 90° = 90 × π/180 = π/2 rad ≈ 1.571 rad. The converter above does this instantly.

What is the difference between degrees and radians?

Degrees divide a circle into 360 parts; radians use arc length (1 rad = angle for which arc = radius). 360° = 2π rad. Radians simplify calculus and physics formulas.

How do I convert radians to degrees?

Multiply radians by 180/π. So π/2 rad = 90°, 1 rad ≈ 57.30°. Example: 2 rad = 2 × 180/π ≈ 114.59°.

What are gradians and when are they used?

Gradians divide the circle into 400 parts. 100 grad = 90°. Used in surveying and some European engineering. 1 grad = 0.9°.

Can I convert arc minutes and arc seconds?

Yes. 1° = 60 arcmin, 1 arcmin = 60 arcsec. So 1° = 3,600 arcsec. Used in astronomy and geodesy. This converter supports arcmin and arcsec.

How accurate is this angle converter?

Conversions use exact math (π/180, etc.). Results are precise. Radians are stored with full floating-point precision.

Angle Converter

Math and physics use radians; maps and construction use degrees. Surveyors sometimes use gradians (400 to a circle), and the military uses mils. A right angle is 90°, π/2 rad, 100 grad, or 1,600 NATO mils — same angle, different numbers.

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Quick Reference: Most Searched Angle Conversions

90° in radiansMost searched

1.571 rad

π rad in degreesHalf circle

180°

180° in radiansStraight

3.142 rad

1 rad in degreesReference

57.30°

45° in radiansRight bisect

0.785 rad

360° in radiansFull circle

6.283 rad

100 grad in degreesSurveying

90°

60 arcmin in degreesExact

1°

Real-World Angle Scale

How these numbers relate to everyday life

0.00000484813681109536rad

1 arcsecond

1″ = 1/3,600 of a degree. Used in astronomy and geodesy.

0.0002908882086657216rad

1 arcminute

1′ = 1/60°. Nautical and celestial navigation.

0.017453292519943295rad

1 degree

1° = π/180 rad. Common in construction, maps, and everyday use.

0.7853981633974483rad

45°

Half a right angle. Common in drafting and diagonal cuts.

1.5707963267948966rad

90° (right angle)

π/2 rad = 90° = 100 grad. Corner of a square.

1rad

1 radian

Arc length = radius. ~57.3°. Preferred in calculus and physics.

3.141592653589793rad

180° (straight)

π rad = 180°. Half turn.

6.283185307179586rad

360° (full circle)

2π rad = 1 turn. One complete rotation.

Who Uses Angle Conversions?

Mathematics & Physics

Formulas for derivatives and trigonometry are simpler in radians. sin(x) and cos(x) in calculus assume x in radians; using degrees gives wrong results unless converted.

sin(π/2) = 1, but sin(90) in degrees interpreted as rad would be wrong. Always use rad for sin/cos in code.

Surveying & Construction

Angles are often in degrees (and decimal degrees) or gradians. Total stations and theodolites may output gradians in some regions; converting to degrees avoids layout errors.

100 grad = 90°. A 50 grad slope = 45°. 1 grad = 0.9°.

Navigation & Aviation

Heading and bearing are in degrees (0–360). Chart work and some instruments use arc minutes. Radians appear in great-circle and geodesic formulas.

Heading 270° = 3π/2 rad = west. 1° of latitude ≈ 60 nautical miles; 1′ ≈ 1 nm.

Graphics & Game Dev

Rendering and rotation APIs often use radians (e.g. CSS, OpenGL, Unity). Design tools may use degrees. Feeding degrees into a radian API rotates by the wrong amount.

rotate(90) in degrees = 1.571 rad. Many libraries expect radians: use deg × π/180.

Military & Ballistics

Mils (milliradians or NATO mils) are used for angular measurement and artillery. 1 NATO mil = 1/6,400 of a circle; 3,200 mils = 180°.

1 mil ≈ 1 m at 1 km. 6,400 NATO mils = 360°. Conversion to degrees: degrees = mils × 9/160.

Did You Know?

A radian is the angle for which the arc length on a circle equals the radius. So a full circle has circumference 2πr and thus 2π radians. That makes derivative formulas like d(sin θ)/dθ = cos θ true only when θ is in radians.

Source: SI Brochure

Gradians (gon) divide the circle into 400 parts instead of 360. So 100 grad = 90°. They were promoted for decimal convenience; adoption is limited to surveying and some European use.

Source: ISO 80000

NATO mil (6,400 per circle) differs from true milliradian (2,000π ≈ 6,283 per circle). Artillery and scopes use NATO mil for "1 mil ≈ 1 m at 1,000 m" rule of thumb.

Source: STANAG

Common Mistakes to Avoid

Using degrees in formulas that expect radians (e.g. sin, cos in code)

Multiply degrees by π/180 before passing to sin/cos/tan. Example: sin(90°) = sin(90 × π/180) = sin(π/2) = 1. In JavaScript: Math.sin(deg * Math.PI / 180).

Confusing arcminutes (angle) with minutes (time)

1 arcminute = 1/60 of a degree (angle). 1 minute = 1/60 of an hour (time). Different quantities. In navigation, both appear: position in degrees and arcminutes, time in hours and minutes.

Treating NATO mil and milliradian as the same

1 NATO mil = 360/6,400° = 0.05625°. 1 milliradian = 180/(1000π)° ≈ 0.0573°. For rough work they are close; for precise conversion use the correct factor.