Convert Gradian (grad) to Turn (tr) instantly. Enter any value and get the result immediately.
grad → tr Converter
| Gradian (grad) | Turn (tr) |
|---|---|
| 0.1 grad | 0.00025 tr |
| 0.5 grad | 0.00125 tr |
| 1 grad | 0.0025 tr |
| 2 grad | 0.005 tr |
| 5 grad | 0.0125 tr |
| 10 grad | 0.025 tr |
| 20 grad | 0.05 tr |
| 50 grad | 0.125 tr |
| 100 grad | 0.25 tr |
| 200 grad | 0.5 tr |
| 500 grad | 1.25 tr |
| 1000 grad | 2.5 tr |
| 5000 grad | 12.5 tr |
| 10000 grad | 25 tr |
Converting gradians to turns is one of the most straightforward angle unit conversions because both units divide a full circle into clean, logical fractions. A full circle equals exactly 400 gradians and exactly 1 turn — so to convert, simply divide the gradian value by 400. Use the converter above for instant results, or follow the formula and examples below.
Step-by-step example — Convert 200 grad to turns:
Step-by-step example — Convert 50 grad to turns:
Step-by-step example — Convert 1000 grad to turns:
Gradian (grad), also written as gon or grade, is a metric unit of angular measurement where a full circle is divided into exactly 400 equal parts. It was developed during the French Revolution as part of the broader metrication effort to bring decimal logic to all measurement systems. Under this system, a right angle equals exactly 100 gradians — making gradian arithmetic especially clean for right-angle geometry. The gradian is the standard unit of angular measurement in professional land surveying, civil engineering, and cartography across many European countries and is natively supported by most scientific calculators (the "GRAD" mode). One gradian equals 0.9 degrees or π/200 radians.
Turn (tr), also known as a revolution, cycle, or full rotation, is a unit of angular measurement representing one complete 360° rotation — from a starting point back to the exact same position. It is symbolized as tr, rev, or simply r depending on the context. One turn equals 360 degrees, 400 gradians, or 2π radians. The turn is widely used in rotational mechanics, electric motor engineering, gearbox design, robotics joint motion, and any application involving spinning or revolving components. It provides the most intuitive way to express complete rotations — "3 turns" is immediately understood as three full spins, while the equivalent "1,080 degrees" or "1,200 gradians" requires mental calculation to visualize.
| Gradians (grad) | Turns (tr) | Equivalent Angle |
|---|---|---|
| 1 grad | 0.0025 tr | 0.9° — 1 survey grade |
| 25 grad | 0.0625 tr | 22.5° — one-sixteenth circle |
| 50 grad | 0.125 tr | 45° — one-eighth circle |
| 100 grad | 0.25 tr | 90° — right angle (quarter turn) |
| 200 grad | 0.5 tr | 180° — straight angle (half turn) |
| 300 grad | 0.75 tr | 270° — three-quarter turn |
| 400 grad | 1 tr | 360° — full circle (one turn) |
| 800 grad | 2 tr | 720° — two full rotations |
| 1000 grad | 2.5 tr | 900° — two and a half rotations |
| 2000 grad | 5 tr | 1800° — five full rotations |
| Property | Gradian (grad) | Turn (tr) |
|---|---|---|
| Full circle value | 400 grad | 1 tr |
| Right angle value | 100 grad | 0.25 tr |
| Straight angle value | 200 grad | 0.5 tr |
| Origin | French Revolution (metric reform) | General rotational mechanics |
| Primary use | Surveying, civil engineering, cartography | Rotational mechanics, robotics, navigation |
| Symbol | grad or gon | tr or rev |
| Decimal-friendly? | Yes — right angle = 100 grad | Yes — full rotation = 1 tr |
One gradian equals exactly 0.0025 turns (1 ÷ 400 = 0.0025). Because a full circle is 400 gradians and also 1 turn, each gradian represents one four-hundredth of a complete rotation.
The formula is: tr = grad ÷ 400. Divide any gradian value by 400 to get the equivalent number of turns. Alternatively, multiply by 0.0025 — both give the same result.
Exactly 400 gradians equal one full turn (one complete 360° rotation). This is the defining relationship between the two units: 400 grad = 1 tr = 360° = 2π radians.
100 grad = 0.25 tr — which is one-quarter of a full rotation, equivalent to a 90° right angle. This is one of the most useful reference points in gradian-based measurement.
A gradian is also called a gon or a grade. The symbol "gon" is the internationally preferred form used in ISO standards and professional surveying literature. In French, the unit is called grade, which is the historical origin of the term.
The gradian system is especially useful in surveying because a right angle equals exactly 100 grad, and a full circle equals exactly 400 grad — both round decimal numbers. This makes arithmetic with right-angle geometry simpler than the degree system (where a right angle = 90°, a non-round number in many calculations). Surveyors can instantly recognize that any angle near 100 grad is approximately a right angle, and that 50 grad represents a 45° bearing — without needing mental conversion of fractional degrees.
Yes — a turn and a revolution refer to exactly the same thing: one complete 360° rotation. The terms are used interchangeably in physics, engineering, and mathematics. "Turn" (tr) is the preferred term in modern SI-adjacent usage and formal mathematical writing, while "revolution" (rev or r) is more commonly used in mechanical engineering contexts such as RPM (revolutions per minute).
1 turn = 400 gradians. Conversely, to convert turns back to gradians, multiply by 400: grad = tr × 400.
This conversion is most commonly needed when combining data from gradian-based surveying instruments with rotation-tracking systems that measure motion in turns or revolutions. For example, a robotic total station may log 2,800 grad of cumulative rotation during a scanning survey — which equals 7 turns — and the rotation counter in the instrument's firmware needs to track complete turns for internal calibration. Similarly, when analyzing cumulative steering input data from vehicles equipped with gradian-calibrated gyroscopes, engineers convert total gradian values to turns to assess how many complete steering cycles occurred during a test run.