At One Place

Turns to radians

1 turn in radians
1 turn = 6.283185 rad
rad = turn × 6.283185307

To convert turns to radians, multiply by 6.283185307. The table below gives the values people look up most often, and the converter works for any number.

Turns to radians table

Common turn values converted to radians.
Turns Radians
1 turn 6.283185
2 turn 12.56637
3 turn 18.84956
4 turn 25.13274
5 turn 31.41593
10 turn 62.83185
15 turn 94.24778
20 turn 125.6637
25 turn 157.0796
30 turn 188.4956
40 turn 251.3274
50 turn 314.1593
75 turn 471.2389
100 turn 628.3185
250 turn 1,570.7963
500 turn 3,141.5927
1,000 turn 6,283.1853

How the conversion works

The relationship is rad = turn × 6.283185307. Both units measure angle, so the conversion is a fixed factor that never changes.

Common questions

How many radians are in one turn?
One turn equals 6.283185 radians. rad = turn × 6.283185307.
How do you convert turns to radians?
Use rad = turn × 6.283185307. So 10 turn is 62.83185 rad.
How many turns are in one radian?
One radian equals 0.15915 turns, which is the reverse of the conversion above.

Related pages

Sources

  1. Guide for the Use of the International System of Units (SP 811) — NIST (Public domain (US Government))
  2. The International System of Units (SI Brochure) — Bureau International des Poids et Mesures
  3. Calculated on this page — At One Place

How these figures are compiled and checked