Fidamen

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, 2025QA PASS — golden 25 / edge 120Run golden-edge-2026-01-23

Governance

Record 3ae3464fa9b7 • Reviewed by Fidamen Standards Committee

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.

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.

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)

F.A.Q.

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

Further resources

Versioning & Change Control

Audit record (versions, QA runs, reviewer sign-off, and evidence).

Record ID: 3ae3464fa9b7

What changed (latest)

v1.0.0 • 2025-11-27 • MINOR

Initial publication and governance baseline.

Why: Published with reviewed formulas, unit definitions, and UX controls.

Public QA status

PASS — golden 25 + edge 120

Last run: 2026-01-23 • Run: golden-edge-2026-01-23

Engine

v1.0.0

Data

Baseline (no external datasets)

Content

v1.0.0

UI

v1.0.0

Governance

Last updated: Nov 27, 2025

Reviewed by: Fidamen Standards Committee (Review board)

Credentials: Internal QA

Risk level: low

Reviewer profile (entity)

Fidamen Standards Committee

Review board

Internal QA

Entity ID: https://fidamen.com/reviewers/fidamen-standards-committee#person

Semantic versioning

  • MAJOR: Calculation outputs can change for the same inputs (formula, rounding policy, assumptions).
  • MINOR: New features or fields that do not change existing outputs for the same inputs.
  • PATCH: Bug fixes, copy edits, or accessibility changes that do not change intended outputs except for previously incorrect cases.

Review protocol

  • Verify formulas and unit definitions against primary standards or datasets.
  • Run golden-case regression suite and edge-case suite.
  • Record reviewer sign-off with credentials and scope.
  • Document assumptions, limitations, and jurisdiction applicability.

Assumptions & limitations

  • Uses exact unit definitions from the Fidamen conversion library.
  • Internal calculations use double precision; display rounding follows the unit's configured decimal places.
  • Not a substitute for calibrated instruments in regulated contexts.
  • Jurisdiction-specific rules may require official guidance.

Change log

v1.0.0 • 2025-11-27 • MINOR

Initial publication and governance baseline.

Why: Published with reviewed formulas, unit definitions, and UX controls.

Areas: engine, content, ui • Reviewer: Fidamen Standards Committee • Entry ID: 938c80f1f0c2