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Convert Degrees to Turns - Angle Converter

This converter translates angular values given in degrees into turns (full revolutions). A turn represents one complete rotation; by definition 1 turn = 360 degrees.

Use this tool for quick unit conversions in physics, engineering, navigation, laboratory setups, and manufacturing where rotations or fractional revolutions are needed.

Results are exact when expressed as fractions (for example 180° = 0.5 turns) and can be displayed to the number of decimal places appropriate for your instrument or documentation requirements.

Updated Nov 27, 2025

Interactive Converter

Convert between degree and turn with precision rounding.

Quick reference table

DegreeTurn
1 °0.0028 turn
5 °0.0139 turn
10 °0.0278 turn
25 °0.0694 turn
50 °0.1389 turn
100 °0.2778 turn

Methodology

The conversion is based on a fixed ratio between angle units: a full rotation (one turn) equals 360 degrees. This is a dimensionless, exact relationship used across metrology and engineering.

For display and documentation, round results according to your instrument resolution and any regulatory or lab SOP requirements. When high precision is required, keep more decimal places or present as a rational fraction (degrees/360).

When converting sensor output or encoder counts into turns, validate against calibration standards and the device datasheet; small systematic offsets from mounting or index errors should be corrected before using converted values in control or compliance reporting.

Worked examples

45° → 45 ÷ 360 = 0.125 turns

180° → 180 ÷ 360 = 0.5 turns

725° → 725 ÷ 360 = 2.013888... turns (wraps to 2.0138889 turns; if you need modulo 1, use 0.0138889 turns)

Key takeaways

Use degrees ÷ 360 to get turns. Prefer fractional notation when exactness matters (e.g., 90° = 1/4 turn).

For instrument readings, apply calibration adjustments first and choose a rounding level compatible with measurement uncertainty or regulatory reporting rules.

Expert Q&A

What is the exact relationship between degrees and turns?

Exactly 1 turn equals 360 degrees, so turns = degrees ÷ 360. This is a definition used universally in metrology and engineering.

How should I round the result?

Round to the number of decimal places consistent with your instrument resolution and the uncertainty budget for your measurement. For engineering drawings or controls, 3–6 significant digits are common; for regulatory reporting follow the applicable standard or SOP.

How do I handle angles greater than 360° or negative degrees?

The mathematical conversion still applies. For wrap-around to the principal turn (0 to 1), take (degrees ÷ 360) modulo 1. Negative angles convert the same way (e.g., -90° = -0.25 turns).

Can I express the result as a fraction?

Yes. Expressing as a fraction preserves exactness: for example 90° = 90/360 = 1/4 turn. Fractions are useful in design documents and when avoiding rounding error.

Do I need to calibrate instruments before converting encoder counts or sensor degrees to turns?

Yes. Calibrate or zero the instrument per manufacturer guidance and lab SOPs before converting outputs. Apply any offset or scale corrections determined during calibration to avoid systematic error in the converted value.

Is this conversion compatible with SI units and metrology guidance?

Angle units such as the degree and the turn are accepted for use with SI. The conversion is a unit definition and aligns with measurement practice; for detailed metrology guidance consult NIST and BIPM resources.

How do turns relate to radians?

One turn equals 2π radians. You can convert via degrees → turns → radians: radians = (degrees ÷ 360) × 2π, or more directly radians = degrees × (π/180).

Sources & citations