Free navigation maths workbench

Calculate distance, speed or time — and see every step

The navigation relationship is distance = speed × time. Enter any two quantities to find the third, convert between common units, then test the method on six authored sailing problems.

Study position, course and speed

Calculator with working

Solve distance, speed or time

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1/6

A yacht travels at 6 kn for 2 hours. How far does it travel?

A knot is one nautical mile per hour. Convert minutes to hours before using the navigation formula, then convert the final answer only when the question asks for a different unit.

What this calculator teaches

A knot is one nautical mile per hour. When distance is in nautical miles and speed is in knots, time must be in hours. Convert minutes to decimal hours before applying the formula, and keep units beside every line of working so an implausible answer is easier to spot.

Find distance

Distance = speed × time

Find speed

Speed = distance ÷ time

Find time

Time = distance ÷ speed

Worked example

A yacht travels 9 M at 6 kn. Time = 9 ÷ 6 = 1.5 hours. Multiply the decimal part by 60: 0.5 × 60 = 30 minutes. The leg therefore takes 1 hour 30 minutes before any allowance or margin.

Common mistakes

  • Treating 1 hour 30 minutes as 1.30 hours instead of 1.5 hours.
  • Mixing kilometres, nautical miles, km/h and knots without converting.
  • Using speed through the water when the question needs speed over the ground.