Sailing Dead Reckoning Calculator

Dead reckoning, or DR, is one of the oldest techniques in navigation. Starting from a known position, you use your heading, speed, and elapsed time to work out where you are now. It needs no GPS (Global Positioning System) and no external fix at all: a compass, a log, and a clock will do.

You will often read that the name is short for “deduced reckoning”. It almost certainly is not. That story first appears in the twentieth century with no earlier trace, while “dead” in the sense of absolute or exact has been in English for centuries and survives in dead ahead, dead level and dead right. Nice story, wrong etymology.

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 = 60 × 1,852 m = 111.12 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. Over ocean passages of many hundreds of miles the error compounds, and the great-circle or Vincenty formulas do better.

2. Passage planning (distance / speed / time). The second 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, about 1.15 statute miles, and, most usefully, it is one minute of latitude. That last fact is why navigators step off distances against the chart’s latitude scale up the side, never the longitude scale along the bottom: a minute of longitude shrinks as you go north, a minute of latitude does not. Leave any one of the three fields blank and the calculator solves for it.

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, and 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 against a landmark, a GPS, or a celestial observation. Used carefully it is still what 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.