Science
Free fall from rest
Estimate how long an object dropped from rest takes to fall through a known height and the speed it reaches just before impact.
Calculators / Science / Projectile motion
Projectile motion calculator
Resolve launch velocity into horizontal and vertical components to estimate projectile range, flight time and height at equal launch and landing elevations.
On this page
Horizontal range40.79m
Flight time2.88s
Maximum height10.2m
Calculator controls
How to calculate
Resolve launch velocity into horizontal and vertical components to estimate projectile range, flight time and height at equal launch and landing elevations.
Horizontal range = v^2*sin(2*a*pi/180)/g m; Flight time = 2*v*sin(a*pi/180)/g s; Maximum height = v^2*sin(a*pi/180)^2/(2*g) m
Worked example
Launch speed (m/s): 20; Launch angle (degrees): 45; Gravity (m/s²): 9.80665.
Horizontal range: 40.79 m; Flight time: 2.88 s; Maximum height: 10.2 m.
Assumptions and limits
Resolve launch velocity into horizontal and vertical components to estimate projectile range, flight time and height at equal launch and landing elevations. Assumes constant gravity, no air resistance, and no initial vertical speed for free fall. Projectile landing height equals launch height.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Resolve launch velocity into horizontal and vertical components to estimate projectile range, flight time and height at equal launch and landing elevations.
When this tool is useful
Horizontal range = v^2*sin(2*a*pi/180)/g m; Flight time = 2*v*sin(a*pi/180)/g s; Maximum height = v^2*sin(a*pi/180)^2/(2*g) m
Understanding your inputs
| Input | What to enter |
|---|---|
| Launch speed (m/s) | Enter a number of at least 0 and no more than 1000000000000. |
| Launch angle (degrees) | Enter a number of at least 0 and no more than 90. |
| Gravity (m/s²) | Enter a number of at least 1e-12 and no more than 1000000000000. |
Frequently asked questions
What assumptions does this calculation use?
Resolve launch velocity into horizontal and vertical components to estimate projectile range, flight time and height at equal launch and landing elevations. Assumes constant gravity, no air resistance, and no initial vertical speed for free fall. Projectile landing height equals launch height.
How is the result calculated?
Horizontal range = v^2*sin(2*a*pi/180)/g m; Flight time = 2*v*sin(a*pi/180)/g s; Maximum height = v^2*sin(a*pi/180)^2/(2*g) m