Convert Radian to Turn
1 radian = 0.1591549 turn (turn). For example, 10 radian = 1.591549 turn and 100 radian = 15.91549 turn. Type any value below to convert radian to turn both ways — it runs entirely in your browser.
Quick answer: Radian to Turn
1 Radian = 0.1591549 Turn (rad → turn). To convert radian to turn, multiply by 0.1591549. To convert turn to radian, multiply by 6.283185. 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-turn questions.
How to convert Radian to Turn
To convert radian to turn, multiply the number of radian by the conversion factor 0.1591549, because 1 rad = 0.1591549 turn. The conversion is linear, so the same factor works for any value — whole numbers, decimals or fractions. For the reverse direction, 1 turn = 6.283185 rad, so you divide by 0.1591549 (or multiply by 6.283185) to turn turn back into radian.
turn = rad × 0.1591549 ·
rad = turn × 6.283185
- Write down the value you want to convert, in radian.
- Multiply it by 0.1591549.
- The result is the same area/length/quantity expressed in turn.
Radian to Turn — worked examples
Each row shows the exact arithmetic so you can follow the conversion step by step. For example, 5 radian is 0.7957747 turn because 5 rad × 0.1591549 = 0.7957747 turn.
| Radian | Calculation | Turn |
|---|---|---|
| 1 rad | 1 rad × 0.1591549 = 0.1591549 turn | 0.1591549 turn |
| 2 rad | 2 rad × 0.1591549 = 0.3183099 turn | 0.3183099 turn |
| 3 rad | 3 rad × 0.1591549 = 0.4774648 turn | 0.4774648 turn |
| 5 rad | 5 rad × 0.1591549 = 0.7957747 turn | 0.7957747 turn |
| 7 rad | 7 rad × 0.1591549 = 1.114085 turn | 1.114085 turn |
| 10 rad | 10 rad × 0.1591549 = 1.591549 turn | 1.591549 turn |
| 12 rad | 12 rad × 0.1591549 = 1.909859 turn | 1.909859 turn |
| 15 rad | 15 rad × 0.1591549 = 2.387324 turn | 2.387324 turn |
| 20 rad | 20 rad × 0.1591549 = 3.183099 turn | 3.183099 turn |
| 25 rad | 25 rad × 0.1591549 = 3.978874 turn | 3.978874 turn |
| 50 rad | 50 rad × 0.1591549 = 7.957747 turn | 7.957747 turn |
| 100 rad | 100 rad × 0.1591549 = 15.91549 turn | 15.91549 turn |
Common Radian to Turn conversions
These are the radian-to-turn 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 = 0.1591549 turn
- 2 radian = 0.3183099 turn
- 2.5 radian = 0.3978874 turn
- 3 radian = 0.4774648 turn
- 4 radian = 0.6366198 turn
- 5 radian = 0.7957747 turn
- 6 radian = 0.9549297 turn
- 7 radian = 1.114085 turn
- 8 radian = 1.27324 turn
- 9 radian = 1.432394 turn
- 10 radian = 1.591549 turn
- 12 radian = 1.909859 turn
- 15 radian = 2.387324 turn
- 20 radian = 3.183099 turn
- 25 radian = 3.978874 turn
- 30 radian = 4.774648 turn
- 50 radian = 7.957747 turn
- 75 radian = 11.93662 turn
- 100 radian = 15.91549 turn
- 200 radian = 31.83099 turn
- 500 radian = 79.57747 turn
- 1000 radian = 159.1549 turn
Radian to Turn conversion chart (both directions)
The chart below converts radian to turn and turn to radian side by side, so it works whichever way you need. 1 radian = 0.1591549 turn, and 1 turn = 6.283185 radian.
| Radian → Turn | Turn → Radian |
|---|---|
| 0.25 rad = 0.03978874 turn | 0.25 turn = 1.570796 rad |
| 0.5 rad = 0.07957747 turn | 0.5 turn = 3.141593 rad |
| 1 rad = 0.1591549 turn | 1 turn = 6.283185 rad |
| 2 rad = 0.3183099 turn | 2 turn = 12.56637 rad |
| 3 rad = 0.4774648 turn | 3 turn = 18.84956 rad |
| 4 rad = 0.6366198 turn | 4 turn = 25.13274 rad |
| 5 rad = 0.7957747 turn | 5 turn = 31.41593 rad |
| 6 rad = 0.9549297 turn | 6 turn = 37.69911 rad |
| 7 rad = 1.114085 turn | 7 turn = 43.9823 rad |
| 8 rad = 1.27324 turn | 8 turn = 50.26548 rad |
| 9 rad = 1.432394 turn | 9 turn = 56.54867 rad |
| 10 rad = 1.591549 turn | 10 turn = 62.83185 rad |
| 12 rad = 1.909859 turn | 12 turn = 75.39822 rad |
| 15 rad = 2.387324 turn | 15 turn = 94.24778 rad |
| 20 rad = 3.183099 turn | 20 turn = 125.6637 rad |
| 25 rad = 3.978874 turn | 25 turn = 157.0796 rad |
| 30 rad = 4.774648 turn | 30 turn = 188.4956 rad |
| 40 rad = 6.366198 turn | 40 turn = 251.3274 rad |
| 50 rad = 7.957747 turn | 50 turn = 314.1593 rad |
| 75 rad = 11.93662 turn | 75 turn = 471.2389 rad |
| 100 rad = 15.91549 turn | 100 turn = 628.3185 rad |
| 150 rad = 23.87324 turn | 150 turn = 942.4778 rad |
| 200 rad = 31.83099 turn | 200 turn = 1,256.637 rad |
| 250 rad = 39.78874 turn | 250 turn = 1,570.796 rad |
| 500 rad = 79.57747 turn | 500 turn = 3,141.593 rad |
| 1000 rad = 159.1549 turn | 1000 turn = 6,283.185 rad |
Radian vs Turn: which is bigger?
A turn is the larger unit: one turn equals 6.283185 radians. Put another way, you need 6.283185 radians to make a single turn.
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 Turn? History, origin and usage
The turn — also called a revolution, cycle or full circle — is simply one complete rotation, equal to 360 degrees or 2π radians. It is the most intuitive angle “unit,” and the German standard DIN 1315 even proposed a symbol for it; the astronomer Fred Hoyle promoted decimal subdivisions (centiturns, milliturns) in 1962.
The turn is the natural unit for rotational frequency — revolutions per minute (rpm) for engines, motors and disk drives — and for counting coil windings and complete cycles. It underlies how rotation is commonly counted in everyday machinery.
Because one turn equals 2π radians, some mathematicians advocate writing 2π as the single Greek letter τ (tau) so a fraction of a turn reads directly as that fraction of τ. An engine redline of, say, 7,000 rpm means 7,000 complete turns of the crankshaft every minute.
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 Turn to other units
One turn (turn) is equal to:
| 1 Turn equals | Unit |
|---|---|
| 6.283185 rad | Radian |
| 360 ° | Degree |
| 400 gon | Gradian |
| 21,600 ′ | Arcminute |
| 1,296,000 ″ | Arcsecond |
Tips for converting Radian to Turn
- To go from radian to turn, multiply by 0.1591549; to go back, divide by 0.1591549 (or multiply by 6.283185).
- For a quick mental estimate, remember that 1 radian ≈ 0.1591549 turn, so 10 radian ≈ 1.591549 turn.
- 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 Turn converter
Type a number into the Radian field and the equivalent in Turn 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 Turn field to convert the other way (turn 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 = 0.1591549 turn), 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-turn 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 turn are in 1 radian?
- 1 radian = 0.1591549 turn (turn). To convert any number of radian to turn, multiply by 0.1591549.
- How do I convert radian to turn?
- Multiply the number of radian by 0.1591549. For example, 10 radian = 10 × 0.1591549 = 1.591549 turn, and 25 radian = 3.978874 turn.
- How many radian are in 1 turn?
- 1 turn = 6.283185 radian. So to convert turn back to radian, multiply by 6.283185.
- What is the formula to convert radian to turn?
- turn = radian × 0.1591549. The reverse formula is radian = turn × 6.283185.
- How much is 100 radian in turn?
- 100 radian = 15.91549 turn. (And 1000 radian = 159.1549 turn.)
- Which is bigger, a radian or a turn?
- A turn is larger: 1 turn = 6.283185 radian.
- Is this radian to turn converter accurate?
- Yes — every value is computed from the exact 0.1591549 turn per rad factor (not rounded look-up tables), and the factors are re-verified automatically on every update.
- Can I convert turn to radian too?
- Yes. The converter works both ways — enter a value in either field. 1 turn = 6.283185 radian.