OceanCalc

Speed Over Ground Calculator

Vector sum of speed through water and current using law of cosines.

Last updated: March 28, 2026

Author: OceanCalc Editorial Team · Publisher: Albor Digital LLC

Speed Over Ground Calculator

Result

Speed over ground (kn)

7.14

Formula

SOG = √(STW² + Vc² + 2·STW·Vc·cos θ)

Overview

The Speed Over Ground Calculator gives you precise nautical results from familiar formulas, with an interface suited to deck and chart-table use.

How to use

To use the Speed Over Ground Calculator, enter your values in the fields above. Results update as you adjust numbers, so you can compare scenarios without leaving the page.

Formula

The relationship behind this tool is: SOG = √(STW² + Vc² + 2·STW·Vc·cos θ)

θ is the angle between velocity vectors of boat through water and water movement (set).

Practical use cases

Typical uses for the Speed Over Ground Calculator include passage planning, briefing crew, converting instrument readouts to chart units, and double-checking mental math when fatigue or weather make errors more likely.

Tips for accuracy

  • Confirm that the units you enter match your chart, GPS, or instrument readout before relying on the Speed Over Ground Calculator.
  • In rough weather or poor visibility, cross-check important results with a second method or a crew member.
  • Treat simplified models (wave height, radar horizon, etc.) as estimates—real conditions vary with fetch, refraction, and equipment.

Practical examples

  • 6 kn STW + 1.5 kn current at 45° → ~7.1 kn SOG (illustrative)

Frequently Asked Questions

  • How accurate is this calculator?

    This calculator uses standard maritime formulas and practical approximations where noted. It is suitable for planning and cross-checks; always verify safety-critical decisions with official references and local conditions.

  • Can I use this on mobile?

    Yes. OceanCalc tools are responsive and work on phones and tablets for quick checks on deck or in the cockpit.

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Results are estimates for educational purposes only and should not be used for real navigation decisions.

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