Calculate wheel-over distance, speed, rate of turn, or course change angle for a waypoint turn by choosing the unknown and entering three values in multiple units.

Ideal constant-radius turn only. Speed and turn rate must describe the same motion. SOG with heading ROT assumes negligible current/drift. Actual helm timing needs vessel-response allowances; this does not establish a safe speed.

Greater than 0° and less than 180°.

Wheel Over Point Formula

This formula gives ideal circular-arc lead measured back from the inbound and outbound track intersection. It assumes an established constant-radius turn tangent to both tracks. Actual helm initiation also requires allowances from vessel manoeuvring data for steering response and turn build-up.

WOP = (v) / (ω)tan((Δ) / (2))

This equation is based on constant-radius turn geometry. The term v / ω gives the turn radius, and the tangent term adjusts that radius for the planned course change angle.

r = (v) / (ω)
WOP = rtan((Δ) / (2))
Variable Meaning Typical Units
WOP Wheel-over distance, or the lead distance before the waypoint along the inbound leg Nautical miles, miles, kilometers, meters, feet
v Speed over ground Knots, mph, km/h, m/s
ω Rate of turn Radians per minute or radians per second
Δ Planned course change angle between the inbound and outbound tracks Degrees or radians
r Turn radius produced by the chosen speed and rate of turn Same distance units used for the result

Unit Conversions That Matter

The main formula requires the turn rate to be in radians per unit time. It also requires the speed and turn rate to use compatible time units. A common mistake is entering speed in knots while using a turn rate in degrees per minute without converting the turn rate first.

ωrad / min = ROTdeg / min × (π) / (180)

If your speed is in knots and your rate of turn is in degrees per minute, the following form gives the wheel-over distance directly in nautical miles:

WOPNM = (3 × SOGₖₙ) / (π × ROTdeg / min)tan((Δ) / (2))

This is often the quickest manual form for marine navigation problems because it avoids converting knots into nautical miles per minute by hand.

How to Calculate Wheel Over Point

  1. Determine the vessel’s speed over ground.
  2. Determine the planned rate of turn.
  3. Determine the course change angle between the current leg and the next leg.
  4. Convert the rate of turn into radians per unit time, or use the nautical-mile form if your inputs are in knots and degrees per minute.
  5. Calculate the turn radius.
  6. Apply the wheel-over formula to get the lead distance before the waypoint.
  7. Measure that distance backward along the inbound leg to locate the wheel-over point.

Because this calculator accepts any three known values, it can also be used in reverse. For example, you can solve for the required rate of turn to keep the maneuver inside a desired lead distance, or solve for the speed implied by the selected geometry and turn rate. This is not an operational speed limit.

Example

Assume a speed over ground of 15 knots, a rate of turn of 10 degrees per minute, and a course change of 90 degrees.

WOP = (3 × 15) / (π × 10)tan((90^°) / (2))
WOP ≈ 1.432 NM

The ideal circular-arc lead is about 1.43 nautical miles before the track intersection, before adding vessel-response allowances. For a 90-degree change of course, the wheel-over distance equals the turn radius, which makes this a useful mental check when reviewing the result.

How Each Input Affects the Result

Change Effect on Wheel-Over Distance Why
Higher speed over ground Increases A faster vessel needs a larger turn radius at the same turn rate
Higher rate of turn Decreases A tighter turn reduces the lead distance required
Larger course change angle Increases A bigger heading change requires more distance to establish the tangent turn geometry
Smaller course change angle Decreases The vessel needs less lead distance to connect the two legs

Practical Notes

  • The result is a planning distance, not a guarantee of exact vessel behavior under every condition.
  • The model assumes constant speed and angular rate in the same reference motion. Using speed over ground with heading-based rate of turn additionally assumes negligible current or changing drift.
  • Real-world wheel-over points may need adjustment for steering response delay, autopilot behavior, vessel loading, draft, nearby channel limits, and local environmental effects.
  • The course change angle should represent the actual change between the inbound and outbound tracks, not the compass heading error or cross-track correction.
  • The geometry is most useful for ordinary course changes greater than zero degrees and less than 180 degrees.

Common Mistakes

  • Using degrees per minute directly in the main formula without converting to radians.
  • Mixing time bases, such as speed per hour with turn rate per second.
  • Confusing waypoint distance with wheel-over distance.
  • Ignoring the difference between ideal geometric lead distance and actual maneuvering performance.

Why This Calculator Is Useful

The calculator compares ideal turn geometries and supplies an algebraic consistency check. It does not verify vessel capability, channel clearance or safe helm timing; use vessel manoeuvring data and the applicable navigation plan for those decisions.