Formula
Gradians = Turns × 400Direct answer
Multiply the entered turns value by 400 to express it in gradians (gon). This converts turn (turn) to gradian (gon) within the documented angle family.
Variables and formula
- Turns (turn): the source value measured in turn.
- Gradians (gon): the same quantity expressed in gradian.
- Conversion factor: 400 gradians per turn.
Gradians = Turns × 400
The generator emits numeric factors with at most 15 significant digits. Calculator results keep up to 10 significant digits for display; this formatting does not increase the precision of the measurement.
Unit definitions and named variants
Source unit: turn (turn). A turn is one complete plane rotation, equal to 360° or 2π rad. Named variant used: Complete plane rotation; the display token ‘turn’ is used by CalcMotive rather than asserting a standardized international symbol. Reference: Bureau International des Poids et Mesures: The International System of Units (SI), 9th edition, version 4.01; National Institute of Standards and Technology: NIST Guide to the SI, Appendix B.8: Factors for Units Listed Alphabetically.
Target unit: gradian (gon). A gradian (gon) divides a full turn into 400 parts, so 1 gon = 0.9° exactly. Named variant used: Plane-angle gradian/gon; not a percentage grade or academic grade. Reference: National Institute of Standards and Technology: NIST Guide to the SI, Appendix B.8: Factors for Units Listed Alphabetically.
The turn-to-gon direction remains inside the angle quantity; it changes the unit label and numerical scale, not the kind of quantity being measured.
Relationship and precision
This route is exact once the documented unit convention is selected; the convention itself must match the source measurement.
- turn relationship: The relationship 1 turn = 360° is exact.
- gon relationship: The terminating degree relationship is exact.
To audit the factor through the family base unit, divide the raw dataset factors 360 by 0.9. The generator emits that quotient once at 15 significant digits as the canonical direct factor 400; runtime calculations do not divide the already-emitted base factors again.
Reproducible example
For 10 turns, 10 × 400 = 4000 gradians. Repeating the same multiplication with the stated factor reproduces the displayed conversion before interface rounding.
Directional scale check
Because one turn contains 400 gradians, the target number is larger than the source number for every positive input. Zero maps to zero, while negative inputs are preserved as signed values under the stated direction convention.
| Source amount | Calculation | Target amount |
|---|---|---|
| 1 turn | 1 × 400 |
400 gon |
| 10 turn | 10 × 400 |
4000 gon |
| 100 turn | 100 × 400 |
40000 gon |
| 1000 turn | 1000 × 400 |
400000 gon |
Interpretation
Read the result as gradians, not turns. A value entered as turn leaves the calculator labelled gon; this directional distinction matters even when the two units describe the same angle quantity.
Assumptions and limitations
- Negative turns are supported and represent full rotations in the opposite direction under the user’s convention.
- Radian and degree are explicitly distinct: one right angle is π/2 rad and 90°, so 1 rad = 180/π degrees and 1° = π/180 rad.
- Signed values are supported, but positive/negative rotational direction depends on the user’s coordinate convention.
Common mistakes
- A turn is not normalized; values greater than one turn remain greater than 360°.
- A right angle is 100 gon, not 90 gon.
Continue within the Angle family
See the Angle conversion hub for its five-unit reference table and all 20 directed routes.
- Reverse the direction: Gradians to Turns
- Compare another angle route: Turns to Degrees
- Compare another angle route: Turns to Radians
- Compare another angle route: Turns to Arcminutes
- Compare another angle route: Gradians to Degrees
Assumptions
- The entered value uses turns exactly as labelled.
- Negative turns are supported and represent full rotations in the opposite direction under the user's convention.
- Rounding and measurement uncertainty remain the user's responsibility.
Sources and methodology
CalcMotive publishes the formula and assumptions so you can decide whether the estimate fits your use case. See our methodology standards.
- The International System of Units (SI), 9th edition, version 4.01; Bureau International des Poids et Mesures; accessed Aug 7, 2026
- NIST Guide to the SI, Appendix B.8: Factors for Units Listed Alphabetically; National Institute of Standards and Technology; accessed Aug 7, 2026