Round-Trip Ground Speed Calculator (Why Wind Always Costs)
Out against the wind, back with it — compute both ground speeds and the round-trip average that proves a headwind is never repaid by its tailwind.
You spend more time in the slow leg than the fast one, so the arithmetic average lies. With wind equal to half your TAS, the round trip averages only 75% of TAS — and at wind = TAS, you never come home.
Formula
⚠️ For flight planning and education only — verify with your POH/AFM, certified instruments and official sources. Not for primary navigation or airworthiness decisions.
Out against the wind, back with it — compute both ground speeds and the round-trip average that proves a headwind is never repaid by its tailwind.
About Round-Trip Ground Speed Calculator (Why Wind Always Costs)
Every student pilot eventually argues that a 25-knot headwind outbound is refunded by the 25-knot tailwind home. This calculator settles it with the harmonic mean: because more minutes are spent in the slow direction, the round-trip average ground speed always falls below TAS, and the time lost grows with the square of the wind fraction. Enter your trip and watch the refund theory lose, in minutes.
How to use Round-Trip Ground Speed Calculator (Why Wind Always Costs)
- 1Enter — sensible defaults are pre-filled so you see a worked result immediately.
- 2Read the live results: .
- 3Check the "With your numbers" line to see the formula average GS = 2·V_out·V_back/(V_out + V_back) — the harmonic mean, always below TAS substituted step by step.
- 4Adjust inputs (or flip the unit toggle) until the scenario matches yours, then copy or share the result.
Why use Round-Trip Ground Speed Calculator (Why Wind Always Costs)?
- ✓Instant, free and private — every calculation runs in your browser, nothing is uploaded
- ✓Built on the published formula average GS = 2·V_out·V_back/(V_out + V_back) — the harmonic mean, always below TAS with sources cited on the page
- ✓You spend more time in the slow leg than the fast one, so the arithmetic average lies. With wind equal to half your TAS, the round trip averages only 75% of TAS — and at wind = TAS, you never come home.
- ✓Switch units, tweak any input and watch every result update live
Frequently asked questions
Why doesn't the tailwind cancel the headwind?+
Time-weighting. The trip average is distance over time, and the into-wind leg eats disproportionate time. Mathematically the average is the harmonic mean 2ab/(a+b), which never exceeds the arithmetic mean and equals it only in calm air. A 120-kt airplane in 25 kt of wind averages 114.8, not 120.
How big is the penalty in practice?+
Proportional to (wind/TAS)²: light wind costs almost nothing (10 kt on 120 → 0.7% slower), but the cost compounds — 40 kt on 120 costs 11%, and 60 kt costs 25%. Slow aircraft pay savagely: the same 25-kt wind that nicks a jet's schedule takes 9% from a Cub's day.
Does this mean route or altitude choice can beat the wind?+
Sometimes meaningfully. Because the penalty is quadratic, halving the wind component (different altitude, a dogleg through gentler flow) quarters the loss. On long round trips it can pay to cruise lower into wind and higher with it — fuel-burn permitting — exactly the optimization airline dispatch performs daily.
What happens as the wind approaches my TAS?+
The outbound leg's time diverges to infinity — the formula's denominator goes to zero, and this calculator shows the average collapsing toward zero. Gliders and paramotor pilots live this edge case routinely: penetration into wind is the binding performance constraint, not stall or structure.
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