Sailing Dead Reckoning Calculator

Dead reckoning is one of the oldest techniques in navigation. Starting from a known position, you use your heading, speed, and elapsed time to estimate where you are now. It does not need GPS or any external fix — just a compass, a log, and a clock. The name probably comes from “deduced reckoning”, shortened over centuries of seafaring use.

This calculator offers two modes. Use whichever matches what you actually need:

1. Position update. Given a starting latitude and longitude, a compass heading (true), a speed, and an elapsed time, work out the new latitude and longitude. This is the real dead-reckoning calculation:

Latitude₂ = Latitude₁ + d × cos(θ) Longitude₂ = Longitude₁ + d × sin(θ) / cos(Latitude₁)

Here θ is the true heading (clockwise from north), d is the distance travelled expressed in degrees of latitude (1° = 60 nautical miles = 1,852 m × 60 ≈ 111.32 km), and the cos(Latitude₁) term corrects for the convergence of longitude lines toward the poles. For short-range coastal navigation this flat-Earth approximation is fine; for ocean passages over many hundreds of nautical miles the small error compounds and the Vincenty formulas or great-circle equations give better accuracy.

2. Passage planning (distance / speed / time). A second, simpler relationship is the bedrock of every passage plan: distance (nm) = speed (knots) × time (hours). One knot is one nautical mile per hour. A nautical mile is 1,852 metres or about 1.15 statute miles, and one minute of latitude on the chart — which is why navigators measure with the chart’s latitude scale, never the longitude scale. Leave any one of the three fields blank and the calculator solves for that one.

A few things real navigators always remember. Dead reckoning gives speed through the water, not over the ground. A two-knot favourable tide adds two knots to your real progress; a foul tide steals just as much. Wind pressure on hull and sails causes leeway, so the course steered and the course made good differ — sometimes by several degrees. And errors compound: every hour of unobserved DR adds uncertainty until you can fix the position with a landmark, GPS, or a celestial observation. Used carefully it is still the foundation a working passage plan rests on; used blindly it puts boats on reefs.

Passage-planning rule-of-thumb. A sailing yacht averages 5 to 7 knots under sail. So:

• 100 nm passage: roughly 14–20 hours
• Overnight (12 h) passage: 60–84 nm
• Offshore 200 nm passage: 28–40 hours

For motoring boats, substitute your cruising speed; for fast cats and racers, scale up.