Aviation & Aeronautics
Intermediate

Rate of Turn

Angular rate of a coordinated turn (radians/s; a standard rate turn is 3°/s).

Formula

ω=gtan⁡ϕv\omega = \dfrac{g\tan\phi}{v}

Variables

\omegaTurn rate
gGravity
\phiBank angle
vTrue airspeed

Example

A standard-rate turn is 3°/s, so a full 360° circle takes exactly 2 minutes.

How it works

This formula gives the angular speed at which an aircraft changes heading while making a coordinated level turn. It comes from balancing the horizontal component of lift against the centripetal acceleration needed to follow a circular path: more bank angle means more sideways lift and a faster turn, while higher true airspeed means the aircraft covers more distance each second and therefore turns more slowly for the same bank.

When to use it

Use this when you need to estimate turn rate from bank angle and airspeed, such as in flight planning, instrument flying, or checking whether a bank angle will produce a standard or non-standard turn. It is especially useful for coordinated turns where altitude is maintained and the turn is not slipping or skidding.

Worked example, step by step

Given: bank angle φ = 20°, true airspeed v = 120 m/s, gravity g = 9.81 m/s² Step 1: Find tan(φ) = tan(20°) ≈ 0.364 Step 2: Substitute into the formula: ω = (g tan φ) / v Step 3: ω = (9.81 × 0.364) / 120 Step 4: ω ≈ 3.57 / 120 = 0.0298 rad/s Step 5: Convert to degrees per second: 0.0298 × 57.3 ≈ 1.71°/s Final answer: the aircraft turns at about 0.030 rad/s, or about 1.7°/s.

Common mistakes to avoid

  • Using indicated airspeed instead of true airspeed without checking whether the approximation is acceptable
  • Forgetting that the bank angle must be in degrees only if your calculator is set to degrees for tan(φ)
  • Applying the formula to uncoordinated turns or climbs/descents where the level-turn assumption does not hold

Did You Know?

A "standard rate" turn is 3° per second — a full 360° circle in exactly two minutes.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026