Horizontal Throw calculator

Enter horizontal speed and edge height. Flight time depends only on h: t = √(2h/g), and range is Z = v₀ t. 6 m/s from 8 m is about 1.28 s and 7.7 m, launch angle 0°.

Inputs

Result

Horizontal speed v₀, Launch height h and g (default 9.81). The result shows up here.

How it works

v₀ h Z
Horizontal throw from height h: flight time depends only on the drop; range Z = v₀·t.

A horizontal throw leaves an edge with v₀ in the horizontal. Fall time t = √(2h/g) does not depend on v₀. Range Z = v₀ t. At 6 m/s and h = 8 m: t ≈ 1.28 s, Z ≈ 7.7 m. Landing v_y is g t ≈ 12.5 m/s. Twice the h is √2 times the time, not two: from 32 m at the same v₀, time ≈ 2.55 s and Z ≈ 15.3 m.

Fields: v₀, h, empty g = 9.81. Results in meters and seconds. No air drag. Launch angle is 0° and you do not type it. A comma and a period are the same h: 8,5 and 8.5.

h must be positive. Typed 0 m gives t = 0 and Z = 0, because there is nothing to fall from. v₀ = 0 is a drop on the spot, Z = 0, time as in free fall. v₀ and h both need numbers before 7.7 m can appear.

A drop with no horizontal v₀ is on the neighbouring page: there you type t and get h. A nonzero angle is on full projectile. This calculator stays at α = 0° and a launch from height h.

Flight time does not speed up when you kick harder horizontally. A larger v₀ only stretches Z. 12 m/s from the same 8 m is still ≈ 1.28 s, but Z ≈ 15.3 m.

Type 6 and 8, leave g empty, click Calculate, and match t ≈ 1.28 s and Z ≈ 7.7 m. The header symbol does not drop you off the edge.

Fall time alone: free fall. Angle other than 0°: full projectile.

How to use

  1. Type horizontal v₀ in m/s, for example 6. That is the component along the edge, not a downward slant.
  2. Type height h in meters, for example 8. Zero meters gives no flight. Leave g blank for Earth.
  3. Click Calculate. 6 m/s and 8 m give t ≈ 1.28 s and Z ≈ 7.7 m. Landing v_y is about 12.5 m/s.
  4. Time depends only on h, not on v₀. Twice the v₀ at the same h doubles Z, time stays put.
  5. With no horizontal v₀, open free fall. An angle other than 0° is on full projectile. Here it stays the edge and a horizontal flight.

Formula

t = √(2h/g)

Z = v0 · t

vy = g · t

Initial velocity is horizontal; launch from height h.

v₀, h, and Z from an edge

A horizontal throw has 0° built in. Time t = √(2h/g) does not depend on v₀. 6 m/s from 8 m is about 1.28 s and Z ≈ 7.7 m.

v₀
Horizontal speed. 12 m/s from the same 8 m is still ≈ 1.28 s, but Z ≈ 15.3 m. Zero gives Z = 0, time as in free fall.
h
Edge height. Zero meters gives t = 0. From 32 m at 6 m/s, time ≈ 2.55 s: four times h, twice t.
Z
Range: Z = v₀ t. Flight time does not speed up when you kick harder horizontally.
t
Flight time from height: t = √(2h/g). Landing v_y is g t, about 12.5 m/s from 8 m.
g
Blank = 9.81 m/s². It sits under the square root in t, not in v₀.

Real-life examples

Example 1

v₀ = 6 m/s, h = 8 m.

Example 2

v₀ = 10 m/s, h = 25 m.

Example 3

v₀ = 8 m/s, h = 20 m.

Example 4

v₀ = 4 m/s, h = 3 m.

Example 5

v₀ = 20 m/s, h = 50 m.

Example 6

v₀ = 3 m/s, h = 2.5 m.

Example 7

v₀ = 8 m/s, h = 20 m, g = 1.62 m/s².

Example 8

v₀ = 5 m/s, h = 1.5 m above water.

Ways to use this calculator

  • You find how far an object goes from 8 m at 6 m/s horizontal.
  • You check that t depends on h, not on v₀.

Related calculators

Fall time from height alone
A vertical drop, no horizontal launch speed.
Energy of the horizontal motion
Kinetic energy from the horizontal launch speed alone.
Free-fall time from h
Fall time from height, no range.
Vertical Throw Calculator
Vertical throw up or down: peak height and the state at time t.
Projectile Range
How far a projectile travels on level ground.

All physics calculators

Frequently asked questions

How much Z at 6 m/s and h = 8 m?

t = √(16/9.81) ≈ 1.28 s. Z = 6 × 1.28 ≈ 7.7 m. Landing v_y ≈ 12.5 m/s.

Does flight time depend on v₀?

No. t = √(2h/g). v₀ only changes Z = v₀ t. 12 m/s from 8 m is still ≈ 1.28 s, but Z ≈ 15.3 m.

Which units do I type?

v₀ in m/s, h in meters, g in m/s². Results in meters and seconds. Empty g = 9.81.

What if h = 0 or v₀ = 0?

h = 0 gives t = 0 and Z = 0. v₀ = 0 gives Z = 0 and the same time as free fall: you drop under the edge.

How is this different from free fall?

Here you have horizontal v₀ and Z. There you type t and get h, start from rest. Fall time from 8 m is the same.

An angle other than 0°?

Open full projectile. This calculator has α = 0°. A slant up or down changes both t and Z.

Is there air drag?

No. Classroom vacuum model. In air, time grows a little and Z shrinks a little.

How much time from 32 m at 6 m/s?

t ≈ 2.55 s, Z ≈ 15.3 m. Four times h, twice t, twice Z. The square sits in t = √(2h/g).

Where is this flight on full projectile?

v₀ = 6, α = 0°, h₀ = 8. The same pair sits on the full-projectile example card.

Does a comma in 8.5 m work?

Yes. 8,5 and 8.5 are the same h. The calculator does not require a period.

Knowledge sources

The formula is the school one. Units follow SI; NIST SP 330 and BIPM define the measures, not your result.

Page updated in 2026.