Apparent Wind Calculator (Sailing and Cycling)
The wind you actually feel on a moving boat or bike — its speed and the angle it comes from — given the true wind and your own speed.
Results
The dashed line marks the value you entered.
What this tool does
The wind felt on a moving craft is the true wind plus the wind created by your own motion, added as vectors. Sailing close to the wind, the apparent wind is stronger and further forward than the true wind, which is why a boat can feel overpowered upwind and become suddenly calm when it turns downwind. A fast boat can sail with the apparent wind well ahead of the beam whatever the true direction. The same applies to a cyclist riding into, across or with the wind. The true wind angle is measured from the bow, from 0° (head to wind) to 180° (dead downwind).
Formula
AWS = √[(V_t cos θ + V_b)² + (V_t sin θ)²] · AWA = atan2(V_t sin θ, V_t cos θ + V_b)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
vt | True wind speed | kn |
ta | True wind angle from the bow (0° = from ahead, 180° = from astern) | ° |
vb | Boat speed | kn |
AW | Apparent wind speed | kn |
AA | Apparent wind angle from the bow | ° |
AR | Apparent wind as a multiple of true wind | × |
CR | Wind component across the boat | kn |
Worked example
- True wind speed12 kn
- True wind angle from the bow (0° = from ahead, 180° = from astern)60 °
- Boat speed6 kn
- Apparent wind speed15.9 kn
- Apparent wind angle from the bow41 °
- Apparent wind as a multiple of true wind1.32 ×
- Wind component across the boat10.4 kn
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.