Sailboat VMG from polar calculator
Sailing at 6.5 knots on a true wind angle of 45 degrees, you close on an upwind mark at 4.596194 knots. Compare angles to see whether pinching or footing pays upwind, and how deep to sail on a run. Free in your browser.
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Worked example
- Boat speed
- 6.5
- True wind angle deg
- 45
- True wind angle rad
- 0.785398
- Vmg windward
- 4.596194
- Vmg leeward
- -4.596194
- Vmg
- 4.596194
Velocity made good (VMG) turns a single polar table point—boat speed at a given true wind angle—into the component of progress toward the wind or toward a leeward mark. Racers, coaches, and performance-sailing tools use VMG to decide whether pinching higher or footing off is faster upwind, and whether to heat up or soak deeper on a run. This sailboat VMG from polar calculator accepts boat speed through the water and true wind angle in degrees, folds the angle into the sailing range zero to one hundred eighty degrees, and returns windward VMG, leeward VMG, the classic signed windward component, absolute VMG, and a progress label of upwind, downwind, or beam. The pure analytic identities match textbook polar analysis: windward VMG equals boat speed times cosine of TWA, and leeward VMG equals boat speed times cosine of one hundred eighty degrees minus TWA.
What sailboat VMG means on a polar diagram
A sailboat performance polar is a family of curves that map true wind angle and true wind speed to expected boat speed through the water for a given sail set and sea state. Reading one point off that polar gives you boat speed at a chosen TWA, but boat speed alone does not say how fast you are closing on an upwind mark or a downwind finish. Velocity made good is the component of that boat-speed vector along the wind axis.
With true wind angle measured from dead into the wind at zero degrees through a beam reach at ninety degrees to dead downwind at one hundred eighty degrees, windward VMG is boat speed multiplied by the cosine of TWA. When TWA is forty-five degrees, cosine is about point seven zero seven, so roughly seventy percent of your speed is progress to windward and the rest is sideways. When TWA is ninety degrees you are on a beam reach and windward VMG is zero even if the boat is flying.
When TWA exceeds ninety degrees the cosine becomes negative, which means you are making negative progress toward the wind—equivalently, positive progress to leeward. Leeward VMG uses the complementary angle one hundred eighty degrees minus TWA so that a deep run near one hundred fifty degrees shows a strong positive leeward component. Racers maximize positive windward VMG on beats and positive leeward VMG on runs; that is how polar software picks target angles for a given wind speed without requiring a full route solver.
What you enter and what you get back
Negative boat speed is rejected because speed is a magnitude—reverse headings are not encoded as negative BSP. Any finite TWA is folded into the closed sailing interval zero through one hundred eighty degrees by taking the angle modulo three hundred sixty and mirroring angles above one hundred eighty, so port and starboard symmetric polars need only one half of the diagram. Numerics are rounded to six decimal places for stable goldens across runtimes.
Example: boat speed six point five at forty-five degrees TWA yields windward VMG about four point six knots and leeward VMG the negative of that magnitude; at one hundred thirty-five degrees the signs flip and leeward progress dominates.
What you can do with it
Race targets from polar table cells
Convert each polar BSP/TWA point into windward and leeward VMG to pick best upwind and downwind target angles for a given true wind speed.
Polar QA and design notebooks
Assert in CI or design spreadsheets that a revised sail inventory improves peak VMG without silently changing units or angle conventions.
FAQ
What true wind angle convention does the calculator use?
TWA is degrees from dead into the wind (0°) through beam (90°) to dead downwind (180°). Values outside 0–180 are folded into that range with port/starboard symmetry.
Why can windward VMG be negative?
When TWA is greater than 90°, cos(TWA) is negative, so you are making progress away from the wind.
What is velocity made good?
It is the part of your boat speed that actually carries you along the wind axis, toward an upwind mark or a downwind finish. Boat speed alone does not show how fast you are closing on the mark.
Why can a slower angle win the beat?
Because windward progress is boat speed times the cosine of the true wind angle. Sailing a little slower but closer to the wind can keep a much larger share of your speed as progress, so you reach the mark sooner.
How does VMG work on a downwind run?
Leeward VMG uses 180 degrees minus the true wind angle, so a deep run shows a strong positive component toward the leeward mark. On runs you look for the angle that gives the highest leeward VMG.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/travel/sailboat-polar-vmg \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"boat_speed":6.5,"true_wind_angle_deg":45}'const res = await fetch("https://api.kit.forhosting.com/travel/sailboat-polar-vmg", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"boat_speed": 6.5,
"true_wind_angle_deg": 45
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/travel/sailboat-polar-vmg",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"boat_speed": 6.5,
"true_wind_angle_deg": 45
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/travel/sailboat-polar-vmg", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"boat_speed":6.5,"true_wind_angle_deg":45}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"boat_speed":6.5,"true_wind_angle_deg":45}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/travel/sailboat-polar-vmg", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"boat_speed": 6.5,
"true_wind_angle_deg": 45
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "travel.sailboat_polar_vmg",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
Input contract, folding rules, and response fields
POST a JSON body with two required finite numbers: boat_speed, the non-negative boat speed through water from your polar or instruments, and true_wind_angle_deg, the true wind angle in degrees. Boat speed may also arrive under aliases speed, bsp, boat_speed_kn, or v; TWA accepts twa, twa_deg, true_wind_angle, angle_deg, or angle. On success the response echoes boat_speed and the folded true_wind_angle_deg, adds true_wind_angle_rad, vmg_windward, vmg_leeward, vmg (the signed windward component used in classic polar tables), vmg_abs, progress as upwind, downwind, or beam, cos_twa, unit set to same_as_boat_speed so knots in yields knots out, and a formula string restating both identities. Missing fields, non-finite values, and non-object bodies fail with invalid_input and are not billed.
Where a polar VMG calculator earns its keep
Charter briefing sites and sailing schools use the tool to teach why the fastest boat speed is not always the best course to the mark: a slightly slower angle with much higher cosine can win the beat. Keep units consistent between boat speed and the VMG you display, pin the rounded fields in automated tests, and you get reproducible windward and leeward components for polar analysis, race debriefs, and educational landings that rank for sailboat VMG calculator without standing up heavyweight performance-sailing software of your own. Regatta teams and coaching apps feed instrument BSP and TWA or polar-lookup values into this endpoint to build target-angle tables, compare sail inventories, and annotate tracks without shipping a full routing engine.
Integration use cases
Onboard coaching and debrief
Feed instrument boat speed and true wind angle into the API mid-leg or after the race to score whether the helm was near maximum VMG.
Technical questions
How do I calculate sailboat VMG from boat speed and true wind angle?
Send non-negative boat_speed and true_wind_angle_deg. Windward VMG is boat_speed × cos(TWA); leeward VMG is boat_speed × cos(180° − TWA). The API returns both plus the signed classic windward vmg field.
What units does the sailboat VMG calculator use?
Any consistent speed unit (knots, m/s, mph). Output VMG fields use the same unit as boat_speed; unit is reported as same_as_boat_speed.
What does the sailboat VMG from polar calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.