Projectile clears wall calculator
Launch at 20 m/s and 45 degrees toward a 5 m wall 30 m away and the path passes at 7.9350375 m, clearing the top by 2.9350375 m. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Speed
- 20
- Angle
- 45
- Wall distance
- 30
- Wall height
- 5
- Gravity
- 9.80665
- Height at wall
- 7.9350375
- Clearance
- 2.9350375
- Angle deg
- 45
- Time to wall
- 2.1213203436
Physics homework, sports drills and game design often ask a single yes-or-no question: if you launch a ball or model rocket at this speed and angle, will it clear that wall before gravity pulls it down? This projectile clears wall calculator answers with ideal vacuum kinematics on flat ground. You supply launch speed, elevation angle, the horizontal distance to the wall and the wall height above the launch level; the tool reports the trajectory height at that distance, the clearance margin, time of flight to the wall plane, and whether the path strictly clears the top. Gravity defaults to standard Earth value so classroom problems work out of the box, or you can override it for lunar and custom worlds.
What the wall-clearance formula actually computes
Ideal projectile motion ignores air resistance, wind, spin and the curvature of the Earth. Under those assumptions the horizontal velocity stays constant while the vertical velocity changes linearly under constant downward acceleration. Eliminating time between the horizontal and vertical position equations yields the height of the trajectory as a function of horizontal distance alone: y of d equals d times the tangent of the launch angle, minus g times d squared over twice v squared times the square of the cosine of the angle.
That expression is exactly the height of the projectile when it is horizontally level with the wall face. If that height is strictly greater than the wall height, the path clears the top; if it is equal, the projectile clips the upper edge; if it is lower—or already negative because the ball would have hit the ground earlier—the wall is not cleared. The derivation assumes launch height zero on level ground, so a cliff launch or a raised platform needs a different root and this capability will not invent one.
Treat the result as the vacuum flat-ground benchmark, then layer drag or terrain separately when realism matters for design work.
How to choose speed, angle, distance and height inputs
Angle is measured above the horizontal in degrees and must lie in the closed interval from zero to ninety. Zero degrees is a pure horizontal throw whose height at any positive distance is below the launch level under the vacuum formula, so positive walls fail. Wall distance and wall height are non-negative lengths in metres measured from the launch point and launch height respectively.
Gravity defaults to nine point eight zero six six five metres per second squared when omitted, matching common engineering tables for Earth; override it for classroom g equals ten problems, lunar gravity or game worlds. Keep units consistent throughout: mixing kilometres per hour for speed with a wall measured in feet produces a mathematically tidy but physically meaningless comparison for your problem statement.
What you can do with it
Physics homework and lab checks
Verify student answers on whether a projectile launched at known speed and angle clears a wall or fence of given height and distance under ideal gravity.
Sports and ballistics rough estimates
Get a quick vacuum-clearance bound for a ball over a goal wall or barrier before adding drag, spin or wind in a more complete model.
Game and simulation parameter setup
Pick launch speeds and angles that clear an obstacle under ideal gravity, then tune drag coefficients against that baseline in a sandbox.
FAQ
What formula does the projectile clears wall calculator use?
It evaluates the ideal trajectory height y(d) = d·tan(θ) − g·d²/(2·v²·cos²(θ)) at the wall distance and compares it to the wall height. Clears is true only when height at the wall is strictly greater than the wall top.
Why is zero launch speed rejected?
A launch speed of zero leaves the projectile at the origin with no trajectory.
Does the calculator include air resistance?
No. Motion is vacuum kinematics with constant gravity and no drag. Real projectiles clear less often; use the result as an upper-bound reference.
Can I set gravity for the Moon or a classroom value of 10?
Yes. Pass a positive gravity in m/s². If you omit the field, standard Earth gravity 9.80665 m/s² is used.
Is the projectile clears wall calculator free?
The browser tool is free and runs entirely on your device.
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/mech/projectile-clears-wall \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"speed":20,"angle":45,"wall_distance":30,"wall_height":5}'const res = await fetch("https://api.kit.forhosting.com/mech/projectile-clears-wall", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"speed": 20,
"angle": 45,
"wall_distance": 30,
"wall_height": 5
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/mech/projectile-clears-wall",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"speed": 20,
"angle": 45,
"wall_distance": 30,
"wall_height": 5
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/mech/projectile-clears-wall", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"speed":20,"angle":45,"wall_distance":30,"wall_height":5}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"speed":20,"angle":45,"wall_distance":30,"wall_height":5}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/mech/projectile-clears-wall", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"speed": 20,
"angle": 45,
"wall_distance": 30,
"wall_height": 5
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "mech.projectile_clears_wall",
"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
How to choose speed, angle, distance and height inputs
Speed is the full launch magnitude in metres per second and must be strictly positive; a zero launch speed is rejected with invalid_input because a stationary object never leaves the origin and cannot clear any wall. Ninety degrees is a pure vertical shot with no horizontal velocity; if the wall sits at a positive distance the request fails rather than inventing a reach time.
Reading the result and using it in homework or pipelines
Positive clearance means the path is above the wall; zero means it hits the top edge; negative means it strikes below the top or would already be underground. Failed validation never charges balance. When air drag, Magnus force or uneven terrain matter, treat this clearance as the vacuum upper-bound reference and compare against your more detailed simulator rather than replacing that model entirely. The response returns a boolean clears flag, the trajectory height at the wall plane, the signed clearance equal to height at wall minus wall height, the echoed inputs, gravity actually used, time to reach the wall plane, plus ground-level range and peak height for context under the same vacuum model. API calls use prepaid KIT balance at the published base price of $0.002 per successful request.