How do you convert degrees to radians?

Multiply the number of degrees by π/180, because 180° equals π radians. For example, 180° = π ≈ 3.1416 radians, and 90° = π/2 ≈ 1.5708 radians. The converter applies this exact factor automatically.

How do you convert radians to degrees?

Multiply the radian value by 180/π, since π radians equal 180°. One radian is therefore about 57.2958°, so 2 radians ≈ 114.59°. It is simply the inverse of the degrees-to-radians factor.

What is a gradian (gon)?

A gradian, also called a gon or grad, is an angle unit where a full circle is 400 gradians, so a right angle is exactly 100 gon and 1 gon = 0.9°. It is used mainly in surveying and geodesy for its clean base-10 arithmetic.

How many arcminutes and arcseconds are in one degree?

One degree contains 60 arcminutes, and each arcminute contains 60 arcseconds, so one degree equals 3600 arcseconds. These fine subdivisions are used in astronomy, navigation and optics to describe very small angles precisely.

Why are radians used instead of degrees in math and physics?

The radian is the SI unit for plane angle and is defined by arc length, so an arc equal to the radius subtends one radian. This link makes calculus and trigonometry cleaner — for instance, derivatives of sine and cosine only work simply when the angle is in radians.

Angle Converter | Free Online Tool

How to use

1.Type the angle you want to convert into the Value field — decimals and negative numbers are allowed.
2.Choose the source unit under "From" and the target unit under "To" (use Swap to reverse them).
3.Read the converted result instantly, plus a table showing the same angle in every unit at once.

About Angle Converter

This angle converter changes any angle between degrees, radians, gradians (gons), turns (revolutions), arcminutes and arcseconds using exact conversion factors, and it runs entirely in your browser with instant results. Type a value, pick the source and target units, and the answer updates as you type — a full table shows the same angle in every unit at once. The core relationships are fixed and precise: 180° = π radians, 360° = 400 gradians = 1 turn, and 1° = 60 arcminutes = 3600 arcseconds. From these, degrees to radians is value × π/180, and radians to degrees is value × 180/π (1 radian ≈ 57.2958°). A degree is 1/360 of a full circle, the everyday unit for navigation, geometry and screen rotation. A radian is the SI unit for plane angle, defined so that an arc equal in length to the radius subtends exactly one radian; because it ties angle directly to arc length, it is the natural choice in calculus, trigonometry, physics and computer graphics, where angular values feed functions like sine and cosine. A gradian, also written gon or grad, divides the right angle into 100 units so a full circle is 400 gon; this base-10 scheme keeps quadrant arithmetic clean and survives in surveying, geodesy and civil engineering, mainly in parts of Europe. A turn, or revolution, is one complete rotation — 360°, 2π radians, or 400 gon — and is handy for describing gears, wheels, phases and periodic motion in whole cycles. Arcminutes and arcseconds subdivide the degree for fine work: one degree splits into 60 arcminutes, and each arcminute into 60 arcseconds, so an arcsecond is 1/3600 of a degree. These tiny units dominate astronomy, optics, telescope resolution, GPS positioning and cartography, where separations of a fraction of a degree matter. Negative angles are valid and represent rotation in the opposite direction; zero converts to zero in every unit; and converting a value to its own unit returns it unchanged. Results are shown to about eight significant figures, so common conversions read cleanly — 180° displays as 3.1415927 radians rather than a noisy floating-point string — while very large or very small values switch to compact scientific notation. Because everything is computed locally with no upload and no server round-trip, the tool is fast, private and works offline once the page has loaded. Whether you are converting degrees to radians for a physics problem, radians to degrees for a plot label, or degrees to arcseconds for an astronomy calculation, the exact factors above guarantee the numbers line up.

Frequently asked questions

How do you convert degrees to radians?: Multiply the number of degrees by π/180, because 180° equals π radians. For example, 180° = π ≈ 3.1416 radians, and 90° = π/2 ≈ 1.5708 radians. The converter applies this exact factor automatically.
How do you convert radians to degrees?: Multiply the radian value by 180/π, since π radians equal 180°. One radian is therefore about 57.2958°, so 2 radians ≈ 114.59°. It is simply the inverse of the degrees-to-radians factor.
What is a gradian (gon)?: A gradian, also called a gon or grad, is an angle unit where a full circle is 400 gradians, so a right angle is exactly 100 gon and 1 gon = 0.9°. It is used mainly in surveying and geodesy for its clean base-10 arithmetic.
How many arcminutes and arcseconds are in one degree?: One degree contains 60 arcminutes, and each arcminute contains 60 arcseconds, so one degree equals 3600 arcseconds. These fine subdivisions are used in astronomy, navigation and optics to describe very small angles precisely.
Why are radians used instead of degrees in math and physics?: The radian is the SI unit for plane angle and is defined by arc length, so an arc equal to the radius subtends one radian. This link makes calculus and trigonometry cleaner — for instance, derivatives of sine and cosine only work simply when the angle is in radians.

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