Degrees to Gradians Calculator

Direct answer

Multiply the entered degrees value by 1.11111111111111 to express it in gradians (gon). This converts degree (°) to gradian (gon) within the documented angle family.

Variables and formula

• Degrees (°): the source value measured in degree.
• Gradians (gon): the same quantity expressed in gradian.
• Conversion factor: 1.11111111111111 gradians per degree.

Gradians = Degrees × 1.11111111111111

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: degree (°). The degree is a long-standing non-SI plane-angle unit with the exact relation 1° = π/180 rad; a full turn is 360°. Named variant used: Degree of plane or phase angle; not degree Celsius or degree Fahrenheit. 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 °-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.

• ° relationship: The base factor is exactly 1 by the family base-unit choice. Conversion to radians involves π and therefore has no finite decimal expansion.
• gon relationship: The terminating degree relationship is exact.

To audit the factor through the family base unit, divide the raw dataset factors 1 by 0.9. The generator emits that quotient once at 15 significant digits as the canonical direct factor 1.11111111111111; runtime calculations do not divide the already-emitted base factors again.

Reproducible example

For 10 degrees, 10 × 1.11111111111111 = 11.1111111111111 gradians. Repeating the same multiplication with the stated factor reproduces the displayed conversion before interface rounding.

Directional scale check

Because one degree contains 1.11111111111111 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.

Interpretation

Read the result as gradians, not degrees. A value entered as ° leaves the calculator labelled gon; this directional distinction matters even when the two units describe the same angle quantity.

Assumptions and limitations

• Negative degrees are supported and represent the opposite rotational direction under the user’s convention.
• This family performs linear unit conversion only; it does not normalize angles to [0, 360), (−180, 180], or another interval.
• 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.

Common mistakes

• The degree symbol alone denotes angle here; °C and °F are temperature units.
• Grade may mean slope in other contexts; this unit is plane angle.

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 Degrees
• Compare another angle route: Degrees to Radians
• Compare another angle route: Degrees to Turns
• Compare another angle route: Degrees to Arcminutes
• Compare another angle route: Gradians to Radians

Assumptions

• The entered value uses degrees exactly as labelled.
• Negative degrees are supported and represent the opposite rotational 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