Ballistic coefficient calculator
A body with twice the ballistic coefficient slows half as fast in the same air. Enter mass, drag coefficient and cross-sectional area to get that number, plus the sectional density, before you model drop and wind drift. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Mass
- 0.01
- Drag coefficient
- 0.295
- Cross sectional area
- 0.0000456
- Ballistic coefficient
- 743.383883437
- Sectional density
- 219.298245614
The ballistic coefficient is the single number that tells you how well a projectile carries its velocity through the air: the higher it is, the less the trajectory is bent and slowed by drag. It combines three things you can measure or look up — the projectile mass, its dimensionless drag coefficient, and its cross-sectional area — into one ratio, mass divided by drag coefficient times area, expressed in kilograms per square metre when you work in SI units. Hunters, target shooters, ballisticians, aerospace students, and game or simulation developers use it to compare bullets, model drop and wind drift, or sanity-check trajectory tables before committing to a full point-mass solver. This calculator takes mass, drag coefficient, and cross-sectional area, and returns the ballistic coefficient plus the sectional density as a useful intermediate. A cross-sectional area of zero or below is physically meaningless and is rejected with a clear validation error instead of producing infinity.
What the ballistic coefficient means and how it is derived
A projectile in flight loses speed because aerodynamic drag decelerates it, and the deceleration from drag scales with the ratio of drag force to mass. The drag force is one half times air density times velocity squared times the drag coefficient times the reference area, so the deceleration is proportional to air density times velocity squared times Cd times A divided by m.
Grouping the projectile-dependent terms gives the ballistic coefficient Cb equals m divided by Cd times A: everything else being equal, a body with twice the Cb decelerates half as fast at the same speed and air density. That is why long, dense, streamlined bullets fly flatter and resist wind better than light, blunt ones of the same calibre.
The form factor is sometimes separated out so the coefficient is written as sectional density divided by a form factor relative to a standard projectile such as G1 or G7, but the mass-over-Cd-times-area definition used here is the fundamental one and needs no reference model. The special case of zero or negative cross-sectional area is rejected with invalid input, because the formula would divide by zero or imply a non-physical geometry, matching the product rule that non-positive area must fail loudly.
Where ballistic coefficient calculations show up in real work
External ballistics software, from phone apps for hunters to research codes, takes a ballistic coefficient and a muzzle velocity and integrates the point-mass equations to predict drop, time of flight, and wind drift; computing the coefficient itself is the first step when you know mass, measured Cd, and calibre but no published figure. Handloaders and competitive shooters compare candidate bullets by coefficient to pick loads that stay supersonic farther downrange.
Small-arms and air-gun enthusiasts convert manufacturer data given in imperial pounds per square inch into SI kilograms per square metre, or back, and need a trustworthy neutral oracle to check their arithmetic. Game and simulation developers use the coefficient to tune projectile behaviour so trajectories feel physically plausible without a full fluid simulation. Aerospace and physics courses assign it as a compact way to rank re-entry capsules, model rockets, or sports balls by their susceptibility to drag.
If you later need full trajectory integration, wind-drift estimation, or conversion between G1 and G7 drag models, treat those as separate capabilities and landings rather than overloading this ballistic coefficient page.
What you can do with it
Bullet comparison for shooters
Rank candidate projectiles by ballistic coefficient from mass, Cd and calibre-derived area to pick loads that shoot flatter and drift less.
Trajectory model inputs
Produce the Cb that point-mass trajectory solvers need when you have measured drag data but no manufacturer-published coefficient.
Teaching external ballistics
Give students one deterministic oracle for Cb = m/(Cd·A) so worksheets, browser demos and auto-graded scripts agree exactly.
FAQ
What formula does this ballistic coefficient calculator use?
Cb = m / (Cd · A): projectile mass divided by the product of the dimensionless drag coefficient and the cross-sectional area. It also returns sectional density m/A as an intermediate.
What happens if the cross-sectional area is zero or negative?
A non-positive area is physically meaningless and would make the formula divide by zero, so it is rejected with a clear error and nothing is charged.
What units does the result come in?
With SI inputs (kilograms and square metres) the ballistic coefficient is in kg/m². Any consistent mass and length units work, and the result scales accordingly.
Where do I find the drag coefficient?
From published drag tables, wind-tunnel data, or manufacturer specifications matched to a drag model such as G1 or G7. Typical values run from about 0.15 for very streamlined shapes to over 1 for blunt bodies.
What does it cost?
The browser tool is free and runs locally.
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/phys/ballistic-coefficient \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"mass":0.01,"drag_coefficient":0.295,"cross_sectional_area":0.0000456}'const res = await fetch("https://api.kit.forhosting.com/phys/ballistic-coefficient", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"mass": 0.01,
"drag_coefficient": 0.295,
"cross_sectional_area": 0.0000456
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/ballistic-coefficient",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"mass": 0.01,
"drag_coefficient": 0.295,
"cross_sectional_area": 0.0000456
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/ballistic-coefficient", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"mass":0.01,"drag_coefficient":0.295,"cross_sectional_area":0.0000456}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"mass":0.01,"drag_coefficient":0.295,"cross_sectional_area":0.0000456}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/ballistic-coefficient", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"mass": 0.01,
"drag_coefficient": 0.295,
"cross_sectional_area": 0.0000456
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.ballistic_coefficient",
"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
What the ballistic coefficient means and how it is derived
Because the computation is a single division, the result is fully deterministic floating-point arithmetic with no random seeds, wall-clock timestamps, network calls, or model drift: identical inputs always yield identical JSON.
What you send and what you get back
Mass is the projectile mass in kilograms, or any consistent mass unit if you keep area consistent too. Drag coefficient is dimensionless and depends on shape and on the drag model it was measured against; typical values are around zero point two nine five for a sleek spitzer bullet on a G7-like curve, around zero point four seven for a smooth sphere, and up to one or more for blunt or flat-based shapes. Cross-sectional area is the projected frontal area in square metres, which for a bullet is pi times the calibre squared over four; a 7.62 millimetre projectile, for example, presents about four point five six times ten to the minus five square metres. Mass and drag coefficient must likewise be positive. Send three required finite positive numbers under the fields mass, drag_coefficient, and cross_sectional_area. Missing fields, non-numeric strings, NaN, and Infinity fail with invalid_input and are not charged. When cross_sectional_area is zero or negative the request fails with a message that non-positive area is invalid, so callers can fix unit conversions rather than silently receive infinity. On success the response echoes the cleaned inputs, ballistic_coefficient as the primary result in mass-per-area units, sectional_density as mass over area without the drag coefficient, a units hint object, method set to ballistic_coefficient, and a short formula string for display. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.
Where ballistic coefficient calculations show up in real work
Because this capability is a pure parse engine, API pricing is the published base of $0.002 per successful item and failed validation does not consume balance.