Premium Converters
Loading
Loading
Loading
Trigonometry-friendly converter for degrees, radians, gradians, turns, arc-minutes, and arc-seconds used in math, GPS, and astronomy.
Unit
Generated on May 23, 2026
Trigonometry-friendly converter for degrees, radians, gradians, turns, arc-minutes, and arc-seconds used in math, GPS, and astronomy.
An angle converter moves between degrees (familiar everyday unit), radians (the math and physics native unit), gradians (surveying and some European engineering), turns (clean for rotation problems), and minutes/seconds of arc (astronomy and precision navigation). While a full circle is 360 degrees, it is also 2π radians, 400 gradians, and exactly 1 turn. Mixing these up causes silent bugs in code — for example, most programming language trigonometric functions (sin, cos, tan) expect radians, not degrees.
Formula
Radians = degrees × π ÷ 180. Degrees = radians × 180 ÷ π. 1 rad ≈ 57.2958°. 1 turn = 360°.Angle conversions usually show up at one of three moments — when you're solving an A-level or B.Eng physics problem and the formula needs radians but your input is in degrees, when you're writing JavaScript or Python code calling Math.sin() and your sprite is rotating to the wrong angle because you forgot to convert from degrees, or when you're reading an astronomy article that quotes positions in arc-seconds and you have no instinct for how small those numbers are. The radian is the mathematician's native unit because it makes calculus and trigonometry clean — the derivative of sin(x) is cos(x) only when x is in radians, full stop. Every programming language's trig functions expect radians; Math.sin(90) returns 0.893, NOT 1.0, because it thinks you mean 90 radians (about 5,156 degrees). Convert first: radians = degrees × π / 180. The degree (360 per circle) won out culturally because the Babylonians used base-60 math and 360 is the friendliest highly composite number for dividing circles into equal parts. Gradians (400 per circle) were a French Revolutionary metric reform that nobody outside surveying ever adopted. Honest take: in everyday Pakistani life, degrees are all you'll ever encounter. The radian becomes urgent the moment you start writing code, solving physics homework, or building anything that rotates.
An angle converter moves between degrees (familiar everyday unit), radians (the math and physics native unit), gradians (surveying and some European engineering), turns (clean for rotation problems), and minutes/seconds of arc (astronomy and precision navigation). While a full circle is 360 degrees, it is also 2π radians, 400 gradians, and exactly 1 turn. Mixing these up causes silent bugs in code — for example, most programming language trigonometric functions (sin, cos, tan) expect radians, not degrees.
A radian is defined as the angle at which the arc length equals the circle's radius. That is why a full circle is exactly 2π radians — its circumference (2πr) divided by r. Radians are the natural unit in calculus: d/dx(sin x) = cos x only when x is in radians. Degrees (360 per circle) originate in Babylonian astronomy, which used base-60 math and mapped nicely to the 360-day year approximation. Gradians (400 per circle) were a French Revolutionary metric reform that never fully caught on except in surveying and some CAD software.
The most-used angle conversions for trigonometry, engineering, and programming.
| Degrees (°) | Radians (rad) | π Form | Gradians | Turns |
|---|---|---|---|---|
| 0 | 0.0000 | 0 | 0 | 0 |
| 30 | 0.5236 | π/6 | 33.33 | 0.0833 |
| 45 | 0.7854 | π/4 | 50 | 0.125 |
| 60 | 1.0472 | π/3 | 66.67 | 0.1667 |
| 90 | 1.5708 | π/2 | 100 | 0.25 |
| 120 | 2.0944 | 2π/3 | 133.33 | 0.333 |
| 180 | 3.1416 | π | 200 | 0.5 |
| 270 | 4.7124 | 3π/2 | 300 | 0.75 |
| 360 | 6.2832 | 2π | 400 | 1 |
A right angle (90°) = π/2 radians ≈ 1.571 rad — the corner of every square.
A full circle (360°) = 2π rad ≈ 6.283 rad — one complete revolution of a wheel.
The sun moves 15° across the sky every hour (360° ÷ 24 h) — the basis for sundials.
A ship's compass typically uses 360° divided into 32 'points' of 11.25° each.
90° equals π/2 radians, or 100 gradians — the right angle used everywhere from construction to robotics.
180° equals π radians (≈ 3.14159) — a straight line and the famous constant in one.
One full turn is 360°, or 2π radians, or 400 gradians — any of which can describe a single rotation.
1 degree equals 60 arc-minutes (60′), and 1 arc-minute equals 60 arc-seconds (60″) — used in astronomy for fine angular measurement.
Earth's rotation is 15° per hour (360° ÷ 24), which equals 0.25° per minute — the basis of timezone width.
A GPS position accurate to 1 arc-second corresponds to about 30 meters on the ground at the equator.
Jump to a ready-made conversion — useful for quick reference and sharing:
Weight Converter
Convert mass and body weight between kilograms, grams, pounds, ounces, and stones for recipes, fitness, and shipping.
Length Converter
Convert distance and height across meters, kilometers, centimeters, miles, yards, feet, and inches with precision factors.
Temperature Converter
Convert Celsius, Fahrenheit, and Kelvin instantly for cooking oven temps, weather, fever readings, and science homework.
Area Converter (PK)
Pakistan real estate area converter for Marla, Kanal, Square Feet, Square Yards, Square Meters, and Acres on plots and farmland.
Volume Converter
Convert capacity across liters, milliliters, US and UK gallons, cups, fluid ounces, tablespoons, teaspoons, and cubic meters.
Speed Converter
Convert speed and velocity between km/h, mph, m/s, knots, and ft/s for driving, running pace, sailing, and physics problems.
Time Converter
Project planning and programming time converter for seconds, minutes, hours, days, weeks, months, and years using Gregorian averages.
Data Storage Converter
Convert digital file sizes between bytes, kilobytes, megabytes, gigabytes, terabytes, and petabytes on the binary 1024 scale.
Browse all Unit calculators & converters
See every tool in this category, plus FAQs and category-specific guides.