Convert Radian to Degree
1 radian = 57.29578 degree (°). For example, 10 radian = 572.9578 degree and 100 radian = 5,729.578 degree. Type any value below to convert radian to degree both ways — it runs entirely in your browser.
Quick answer: Radian to Degree
1 Radian = 57.29578 Degree (rad → °). To convert radian to degree, multiply by 57.29578. To convert degree to radian, multiply by 0.01745329. 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 radian-to-degree questions.
How to convert Radian to Degree
To convert radian to degree, multiply the number of radian by the conversion factor 57.29578, because 1 rad = 57.29578 °. The conversion is linear, so the same factor works for any value — whole numbers, decimals or fractions. For the reverse direction, 1 ° = 0.01745329 rad, so you divide by 57.29578 (or multiply by 0.01745329) to turn degree back into radian.
° = rad × 57.29578 ·
rad = ° × 0.01745329
- Write down the value you want to convert, in radian.
- Multiply it by 57.29578.
- The result is the same area/length/quantity expressed in degree.
Radian to Degree — worked examples
Each row shows the exact arithmetic so you can follow the conversion step by step. For example, 5 radian is 286.4789 degree because 5 rad × 57.29578 = 286.4789 °.
| Radian | Calculation | Degree |
|---|---|---|
| 1 rad | 1 rad × 57.29578 = 57.29578 ° | 57.29578 ° |
| 2 rad | 2 rad × 57.29578 = 114.5916 ° | 114.5916 ° |
| 3 rad | 3 rad × 57.29578 = 171.8873 ° | 171.8873 ° |
| 5 rad | 5 rad × 57.29578 = 286.4789 ° | 286.4789 ° |
| 7 rad | 7 rad × 57.29578 = 401.0705 ° | 401.0705 ° |
| 10 rad | 10 rad × 57.29578 = 572.9578 ° | 572.9578 ° |
| 12 rad | 12 rad × 57.29578 = 687.5494 ° | 687.5494 ° |
| 15 rad | 15 rad × 57.29578 = 859.4367 ° | 859.4367 ° |
| 20 rad | 20 rad × 57.29578 = 1,145.916 ° | 1,145.916 ° |
| 25 rad | 25 rad × 57.29578 = 1,432.394 ° | 1,432.394 ° |
| 50 rad | 50 rad × 57.29578 = 2,864.789 ° | 2,864.789 ° |
| 100 rad | 100 rad × 57.29578 = 5,729.578 ° | 5,729.578 ° |
Common Radian to Degree conversions
These are the radian-to-degree values people look up most often. Every figure is computed from the exact factor, so you can rely on them for quick reference:
- 1 radian = 57.29578 degree
- 2 radian = 114.5916 degree
- 2.5 radian = 143.2394 degree
- 3 radian = 171.8873 degree
- 4 radian = 229.1831 degree
- 5 radian = 286.4789 degree
- 6 radian = 343.7747 degree
- 7 radian = 401.0705 degree
- 8 radian = 458.3662 degree
- 9 radian = 515.662 degree
- 10 radian = 572.9578 degree
- 12 radian = 687.5494 degree
- 15 radian = 859.4367 degree
- 20 radian = 1,145.916 degree
- 25 radian = 1,432.394 degree
- 30 radian = 1,718.873 degree
- 50 radian = 2,864.789 degree
- 75 radian = 4,297.183 degree
- 100 radian = 5,729.578 degree
- 200 radian = 11,459.16 degree
- 500 radian = 28,647.89 degree
- 1000 radian = 57,295.78 degree
Radian to Degree conversion chart (both directions)
The chart below converts radian to degree and degree to radian side by side, so it works whichever way you need. 1 radian = 57.29578 degree, and 1 degree = 0.01745329 radian.
| Radian → Degree | Degree → Radian |
|---|---|
| 0.25 rad = 14.32394 ° | 0.25 ° = 0.004363323 rad |
| 0.5 rad = 28.64789 ° | 0.5 ° = 0.008726646 rad |
| 1 rad = 57.29578 ° | 1 ° = 0.01745329 rad |
| 2 rad = 114.5916 ° | 2 ° = 0.03490659 rad |
| 3 rad = 171.8873 ° | 3 ° = 0.05235988 rad |
| 4 rad = 229.1831 ° | 4 ° = 0.06981317 rad |
| 5 rad = 286.4789 ° | 5 ° = 0.08726646 rad |
| 6 rad = 343.7747 ° | 6 ° = 0.1047198 rad |
| 7 rad = 401.0705 ° | 7 ° = 0.122173 rad |
| 8 rad = 458.3662 ° | 8 ° = 0.1396263 rad |
| 9 rad = 515.662 ° | 9 ° = 0.1570796 rad |
| 10 rad = 572.9578 ° | 10 ° = 0.1745329 rad |
| 12 rad = 687.5494 ° | 12 ° = 0.2094395 rad |
| 15 rad = 859.4367 ° | 15 ° = 0.2617994 rad |
| 20 rad = 1,145.916 ° | 20 ° = 0.3490659 rad |
| 25 rad = 1,432.394 ° | 25 ° = 0.4363323 rad |
| 30 rad = 1,718.873 ° | 30 ° = 0.5235988 rad |
| 40 rad = 2,291.831 ° | 40 ° = 0.6981317 rad |
| 50 rad = 2,864.789 ° | 50 ° = 0.8726646 rad |
| 75 rad = 4,297.183 ° | 75 ° = 1.308997 rad |
| 100 rad = 5,729.578 ° | 100 ° = 1.745329 rad |
| 150 rad = 8,594.367 ° | 150 ° = 2.617994 rad |
| 200 rad = 11,459.16 ° | 200 ° = 3.490659 rad |
| 250 rad = 14,323.94 ° | 250 ° = 4.363323 rad |
| 500 rad = 28,647.89 ° | 500 ° = 8.726646 rad |
| 1000 rad = 57,295.78 ° | 1000 ° = 17.45329 rad |
Radian vs Degree: 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 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.
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.
Convert 1 Radian to other units
It can help to see a radian next to the other units it is commonly compared with. One radian (rad) is equal to:
| 1 Radian equals | Unit |
|---|---|
| 57.29578 ° | Degree |
| 63.66198 gon | Gradian |
| 0.1591549 turn | Turn |
| 3,437.747 ′ | Arcminute |
| 206,264.8 ″ | Arcsecond |
Convert 1 Degree to other units
One degree (°) is equal to:
| 1 Degree equals | Unit |
|---|---|
| 0.01745329 rad | Radian |
| 1.111111 gon | Gradian |
| 0.002777778 turn | Turn |
| 60 ′ | Arcminute |
| 3,600 ″ | Arcsecond |
Tips for converting Radian to Degree
- To go from radian to degree, multiply by 57.29578; to go back, divide by 57.29578 (or multiply by 0.01745329).
- For a quick mental estimate, remember that 1 radian ≈ 57.29578 degree, so 10 radian ≈ 572.9578 degree.
- 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 Radian to Degree converter
Type a number into the Radian field and the equivalent in Degree 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 Degree field to convert the other way (degree to radian). 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 rad = 57.29578 °), 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 radian-to-degree conversions because a small rounding error in a published table compounds quickly at larger quantities; computing from the exact factor avoids that.
Sources
- BIPM — The International System of Units (SI Brochure) — the defining document for the SI, published by the International Bureau of Weights and Measures. It fixes the base unit that this conversion resolves to, which is why the factor here can be exact rather than approximate.
- NIST — Definitions of the SI base units — the US National Institute of Standards and Technology reference for the SI base units, used here as an independent cross-check on the base-unit definition.
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 degree are in 1 radian?
- 1 radian = 57.29578 degree (°). To convert any number of radian to degree, multiply by 57.29578.
- How do I convert radian to degree?
- Multiply the number of radian by 57.29578. For example, 10 radian = 10 × 57.29578 = 572.9578 degree, and 25 radian = 1,432.394 degree.
- How many radian are in 1 degree?
- 1 degree = 0.01745329 radian. So to convert degree back to radian, multiply by 0.01745329.
- What is the formula to convert radian to degree?
- degree = radian × 57.29578. The reverse formula is radian = degree × 0.01745329.
- How much is 100 radian in degree?
- 100 radian = 5,729.578 degree. (And 1000 radian = 57,295.78 degree.)
- Which is bigger, a radian or a degree?
- A radian is larger: 1 radian = 57.29578 degree.
- Is this radian to degree converter accurate?
- Yes — every value is computed from the exact 57.29578 ° per rad factor (not rounded look-up tables), and the factors are re-verified automatically on every update.
- Can I convert degree to radian too?
- Yes. The converter works both ways — enter a value in either field. 1 degree = 0.01745329 radian.