Speed Over Ground Calculator
Updated recently with improved calculation accuracy and expanded examples.
Vector sum of speed through water and current using law of cosines.
Last updated: August 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)What is the Speed Over Ground Calculator?
Vector sum of speed through water and current using law of cosines.
knot
A knot is a unit of speed equal to one nautical mile per hour (1.852 km/h). Marine wind, boat speed, and current are usually given in knots.
Related Maritime Calculators
Overview
A knot is a unit of speed equal to one nautical mile per hour (1.852 km/h). A Speed Over Ground Calculator is used in maritime navigation to perform precise calculations based on established nautical formulas. This tool allows you to apply your inputs to the stated nautical relationships using accurate and standardized methods.
Key takeaways
- Speed Over Ground Calculator — A knot is a unit of speed equal to one nautical mile per hour (1.852 km/h).
- Formula — θ is the angle between velocity vectors of boat through water and water movement (set).
- How to use — Enter numbers in the fields above; results update as you change inputs.
How to use
Enter numbers in the fields above; results update as you change inputs.
Formula
Core relationship: 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
Speed Over Ground Calculator: passage planning, crew briefings, instrument-to-chart unit checks, and verifying mental math when tired or in rough weather.
Tips for accuracy
- Match input units to your chart, GPS, or instrument before trusting the Speed Over Ground Calculator.
- Cross-check important outputs with a second method or crew when visibility or motion is poor.
- Treat simplified models (waves, radar horizon, etc.) as estimates; real conditions vary.
Practical examples
- 6 kn STW + 1.5 kn current at 45° → ~7.1 kn SOG (illustrative)
Frequently Asked Questions
How accurate is this calculator?
It uses standard maritime formulas and noted approximations. Use it for planning and checks; confirm safety-critical decisions with official sources.
Can I use this on mobile?
Yes. Layouts are responsive for phones and tablets on deck or in the cockpit.
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These calculations are based on standard maritime navigation formulas used in seamanship, chart navigation, and marine route planning.
Results are estimates for educational purposes only and should not be used for real navigation decisions.