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Convert Calc

Turns to Gradians Converter

Enter a value to instantly convert between angle units.

Precision4 dp

1 Turn = 400 Gradian

Key Formulas

Degree → Radian

rad = ° × 0.0174533

Radian → Degree

° = rad × 57.2958

Degree → Gradian

grad = ° × 1.11111

Gradian → Degree

° = grad × 0.9

Formula

gradians = turns × 400

Rotary encoders and motor controllers in automated survey equipment express total rotation in turns or revolutions. European and Middle Eastern surveying software expects angle input in gradians, where a right angle is 100 grad and a full circle is 400 grad. A robotic total station that has panned 0.25 turns to sight a new benchmark must enter 100 grad into the gradian-based coordinate computation. The round numbers in the gradian system — 100 grad = 90°, 200 grad = 180° — simplify decimal arithmetic in surveying calculations.

Source: ISO 80000-3:2019 (Quantities and units — Space and time)

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Frequently Asked Questions

Real-World Examples

Quarter turn — 100 grad (90°). A total station panning to a benchmark at a right angle to the backsight enters exactly 100 grad in gradian-mode software.

0.25 tr = 100 grad

Half turn — 200 grad (180°). A reversing observation in surveying: the instrument has turned 200 grad from the starting direction.

0.5 tr = 200 grad

One full turn — 400 grad (360°). The full-circle equivalence in the gradian system, used when calibrating a rotary encoder to gradian output.

1 tr = 400 grad

One-eighth turn — 50 grad (45°). The diagonal of a rectangular survey plot, entered as 50 grad for a gradian-mode traverse calculation.

0.125 tr = 50 grad