Angle Converter
Convert between degrees, radians, gradians, and turns.
What Is the Angle Converter?
The Angle Converter converts between degrees, radians, gradians (grads), arcminutes, arcseconds, and turns (revolutions). Enter a value in any angle unit to instantly convert to all others — essential for trigonometry, navigation, surveying, and engineering calculations.
Formula
How to Use
Enter an angle value in any supported unit: degrees, radians, gradians, arcminutes ('), arcseconds (''), or turns. The converter displays all equivalent values simultaneously, updated in real time.
Example Calculation
90°: = π/2 ≈ 1.5708 rad = 100 grad = 1/4 turn = 5400 arcminutes = 324,000 arcseconds. 1 radian: ≈ 57.296° = 63.662 grad = 3437.75 arcminutes.
Understanding Angle Converter
Angles can be measured in multiple units depending on the application. Degrees (°) are the most familiar unit in everyday use, dividing a full circle into 360 equal parts — a number chosen by the Babylonians for its high divisibility. Radians, the SI unit of angle, define angles by the ratio of arc length to radius, making them natural for mathematical analysis.
The conversion between degrees and radians — multiplying by π/180 — is one of the most frequently used mathematical conversions in science and engineering. Forgetting to convert is a common source of computational errors in trigonometric calculations. This converter makes the translation instant and error-free.
In navigation, angles are often expressed in degrees, minutes, and seconds (DMS) for latitude and longitude (e.g., 40°26'46''N). Astronomers use arcseconds to measure stellar parallax (1 parsec = 1 arcsecond parallax shift). Engineers working with machine tools may use gradians for their decimal-friendly right-angle measurement.
Frequently Asked Questions
Why are there multiple angle units?
Degrees (360° circle) come from ancient Babylonian base-60 mathematics. Radians are the natural mathematical unit (arc length = radius × angle in rad). Gradians (400-grad circle) were introduced during the French Revolution for decimal compatibility.
When should I use radians?
Radians are required in calculus and most physics formulas. sin(x) differentiation gives cos(x) only when x is in radians. Most programming languages (Math.sin, etc.) take radians as input.
What is an arcminute and arcsecond?
1 degree = 60 arcminutes ('), 1 arcminute = 60 arcseconds ('). Arcseconds are used in astronomy (angular size of celestial objects) and high-precision surveying. 1 arcsecond on Earth's surface ≈ 31 meters.
What is the gradian (grad)?
One gradian = 1/400 of a full circle = 0.9°. Introduced by the French to make right angles exactly 100 grad. Used in some European surveying traditions and on some scientific calculators.
Is this converter free?
Yes, completely free with no account required.