HomeUnit Conversion › Radians to Turns (revolutions)

Radians to Turns (revolutions) (rad to turn)

Convert radians to turns (revolutions): 1 rad = 0.159155 turn. Exact conversion factor, formula, 22-row table and worked examples, with JSON API and MCP access.

Formula

1 rad = 0.159155 turn

turns (revolutions) = radians × 0.1591549431 — reverse: radians = turns (revolutions) × 6.283185307

The factor is derived from the SI definitions of both units (base unit: rad) as listed in NIST SP 811; results on this page are shown to 6 significant figures, the API returns up to 12.

Worked examples

Radians to turns (revolutions) conversion table

Radians (rad)Turns (revolutions) (turn)
10.159155
20.31831
30.477465
40.63662
50.795775
60.95493
71.11408
81.27324
91.43239
101.59155
152.38732
203.1831
253.97887
304.77465
406.3662
507.95775
7511.9366
10015.9155
20031.831
25039.7887
50079.5775
1000159.155

FAQ

How many turns (revolutions) are in one radian?

1 rad = 0.159155 turn. The factor comes from the SI definitions of both units (NIST SP 811 / BIPM), so it is exact or correct to at least 10 significant figures.

What is the formula to convert radians to turns (revolutions)?

Multiply the value in radians by 0.1591549431: turns (revolutions) = radians × 0.1591549431. For example, 5 rad = 0.795775 turn.

How do I convert turns (revolutions) back to radians?

Multiply by the inverse factor 6.283185307 (radians = turns (revolutions) × 6.283185307), or use the turns (revolutions)-to-radians page.

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