Convert Degree to Radian

Quick answer: Degree to Radian

1 Degree = 0.01745329Radian (° → rad). To convert degree to radian, multiply by 0.01745329. To convert radian to degree, multiply by 57.29578. The converter at the top does this instantly and both ways; the sections below give the formula, worked examples, a full conversion chart and answers to the most common degree-to-radian questions.

How to convert Degree to Radian

To convert degree to radian, multiply the number of degree by the conversion factor 0.01745329, because 1 ° = 0.01745329rad. The conversion is linear, so the same factor works for any value — whole numbers, decimals or fractions. For the reverse direction, 1 rad = 57.29578°, so you divide by 0.01745329 (or multiply by 57.29578) to turn radian back into degree.

rad = ° × 0.01745329  ·  ° = rad × 57.29578

1. Write down the value you want to convert, in degree.
2. Multiply it by 0.01745329.
3. The result is the same area/length/quantity expressed in radian.

Degree to Radian — worked examples

Each row shows the exact arithmetic so you can follow the conversion step by step. For example, 5degree is 0.08726646radian because 5 ° × 0.01745329 = 0.08726646 rad.

Common Degree to Radian conversions

These are the degree-to-radian values people look up most often. Every figure is computed from the exact factor, so you can rely on them for quick reference:

• 1 degree = 0.01745329 radian
• 2 degree = 0.03490659 radian
• 2.5 degree = 0.04363323 radian
• 3 degree = 0.05235988 radian
• 4 degree = 0.06981317 radian
• 5 degree = 0.08726646 radian
• 6 degree = 0.1047198 radian
• 7 degree = 0.122173 radian
• 8 degree = 0.1396263 radian
• 9 degree = 0.1570796 radian
• 10 degree = 0.1745329 radian
• 12 degree = 0.2094395 radian
• 15 degree = 0.2617994 radian
• 20 degree = 0.3490659 radian
• 25 degree = 0.4363323 radian
• 30 degree = 0.5235988 radian
• 50 degree = 0.8726646 radian
• 75 degree = 1.308997 radian
• 100 degree = 1.745329 radian
• 200 degree = 3.490659 radian
• 500 degree = 8.726646 radian
• 1000 degree = 17.45329 radian

Degree to Radian conversion chart (both directions)

The chart below converts degree to radian and radian to degree side by side, so it works whichever way you need. 1 degree = 0.01745329radian, and 1 radian = 57.29578degree.

Degree vs Radian: which is bigger?

A radian is the larger unit: one radian equals 57.29578 degrees. Put another way, you need 57.29578 degrees to make a single radian.

What is a Degree? History, origin and usage

Dividing a circle into 360 degrees traces back to Babylonian astronomy and its base-60 (sexagesimal) number system, reinforced by the roughly 360-day ancient year in which the Sun seemed to advance about one degree each day. The number 360 was also prized for being divisible by so many factors.

The degree is the everyday angle unit for navigation, geography (latitude and longitude), construction, geometry teaching and most practical measurement. Its symbol is the small raised circle (°), and it subdivides into arcminutes and arcseconds.

360 is unusually divisible — it splits evenly by every whole number from 1 to 10 except 7 — which made it convenient long before modern arithmetic. A full circle is 360°, a right angle is 90°, and a single degree divides into 60 arcminutes.

What is a Radian? History, origin and usage

The radian is the angle subtended at a circle’s centre by an arc equal in length to the radius — a concept developed by Roger Cotes around 1714, who recognised its naturalness, though the word “radian” only appeared in print in 1873 in exam questions set by James Thomson at Queen’s College, Belfast. Leonhard Euler had effectively adopted radian measure as early as 1765.

The radian is the SI unit of angle and the natural choice throughout mathematics, physics and engineering, because angular velocity, rotational motion and wave equations come out cleanly only in radians. Calculators and programming languages expect trigonometric functions in radians by default.

A full turn is 2π radians, so one radian is about 57.2958 degrees. Radians make calculus elegant: the derivative of sine equals cosine only when the angle is measured in radians — in degrees an awkward conversion factor appears.

Convert 1 Degree to other units

It can help to see a degree next to the other units it is commonly compared with. One degree (°) is equal to:

Convert 1 Radian to other units

One radian (rad) is equal to:

Tips for converting Degree to Radian

• To go from degree to radian, multiply by 0.01745329; to go back, divide by 0.01745329 (or multiply by 57.29578).
• For a quick mental estimate, remember that 1 degree ≈ 0.01745329 radian, so 10 degree ≈ 0.1745329 radian.
• The converter above keeps full precision; the tables round for readability, so use the tool for exact figures.
• Both fields update live as you type — change either side to convert in that direction.

How to use this Degree to Radian converter

Type a number into the Degree field and the equivalent in Radian appears instantly — there is no “convert” button to press and nothing is sent to a server, so it works offline once the page has loaded and is safe for any data. You can also type into the Radian field to convert the other way (radian to degree). Use the swap control to flip the two units, and copy the result with a single click. Because the calculation runs in your browser with full floating-point precision, the converter is more exact than the rounded figures shown in the reference chart above — use the chart for quick look-ups and the tool for precise work.

Accuracy and method

Every figure on this page — the formula, the worked examples, the conversion chart and the “convert to other units” tables — is computed from a single verified conversion factor (1 ° = 0.01745329rad), never copied from a hand-typed lookup table that could drift. That factor is derived from each unit’s definition in terms of a common base unit, and an automated check re-verifies all of the site’s factors on every update, so the numbers here stay correct over time. This matters for degree-to-radian conversions because a small rounding error in a published table compounds quickly at larger quantities; computing from the exact factor avoids that.

Angle factors are exact, anchored to the radian: a full turn = 2π rad = 360° = 400 gon, 1° = 60 arcminutes, 1 arcminute = 60 arcseconds. So the live tool and every number on this page always agree.

Frequently asked questions

How many radian are in 1 degree?

1 degree = 0.01745329 radian (rad). To convert any number of degree to radian, multiply by 0.01745329.

How do I convert degree to radian?

Multiply the number of degree by 0.01745329. For example, 10 degree = 10 × 0.01745329 = 0.1745329 radian, and 25 degree = 0.4363323 radian.

How many degree are in 1 radian?

1 radian = 57.29578 degree. So to convert radian back to degree, multiply by 57.29578.

What is the formula to convert degree to radian?

radian = degree × 0.01745329. The reverse formula is degree = radian × 57.29578.

How much is 100 degree in radian?

100 degree = 1.745329 radian. (And 1000 degree = 17.45329 radian.)

Which is bigger, a degree or a radian?

A radian is larger: 1 radian = 57.29578 degree.

Is this degree to radian converter accurate?

Yes — every value is computed from the exact 0.01745329 rad per ° factor (not rounded look-up tables), and the factors are re-verified automatically on every update.

Can I convert radian to degree too?

Yes. The converter works both ways — enter a value in either field. 1 radian = 57.29578 degree.

Related rotation conversions

• Radian to Degree
• Degree to Gradian
• Gradian to Degree
• Turn to Degree
• Degree to Turn
• Radian to Turn
• Turn to Radian
• Degree to Arcminute
• Arcminute to Degree
• Degree to Arcsecond

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