Start with units
Check that quantities belong together before calculating. Use the converter when a problem gives measurements in different units.
VECTOR LAB
WorkspacePhysicsProjectile
local computation
Your first experiment
Choose a formula. Change a value. Inspect what moves.
The result, worked steps, and live model stay connected. Start with any subject—the calculations stay on this device.
Projectile Motion Calculator
Resolve launch velocity into horizontal v₀ cos θ and vertical v₀ sin θ components. Horizontal velocity stays constant while gravity changes the vertical velocity.
Worked example: A 20 m/s launch at 45° with g = 9.81 m/s² travels about 40.775 m, stays airborne about 2.883 s, and reaches about 10.194 m above its launch height.
Assumptions and units: The landing height equals the launch height. Gravity is uniform, the angle is measured above horizontal, and air resistance, wind, and Earth curvature are ignored.
Read the full lesson and self-check calculated in real time
Select a formula, tune the variables, and see the model respond. No black box — just a clearer way to think.
active module
Physics / Projectile
Library
Physics formulas
Fundamentals
Mechanics
Energy
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Electricity
Physics / instrument
Projectile motion
Launch an object and follow its position, velocity, and energy.
y = v₀sin(θ)t − ½gt²
animated trajectory
flight
3.274 s
range
58.394 m
peak
13.145 m
model notes
Horizontal motion stays steady while gravity trades kinetic energy for potential energy, then gives it back.
Flight mode
live / looping
Object type
Projectile motion
Change speed, angle, or gravity to rebuild the flight path instantly.
Live result
58.394m
time scope
Live response · 0–3.274 seconds
Export selected trace · height (m)
final height
0 m
final speed
24 m/s
final kinetic energy
288 J
final potential energy
0 J
step by step
- 01Resolve 24 m/s into horizontal and vertical components at 42°
- 02Range = (24)² × sin(2 × 42°) ÷ 9.81
- 03Horizontal range = 58.394 m; mass 1 kg sets the energy scale
unit converter
Converted result
100 cm
Learn from the result
A calculator that explains the numbers
Use Vector Lab as a visual study companion: change one variable, inspect the model, and connect the substitution steps to the result. The best way to learn a formula is to see which inputs actually control it.
Study the formulas: lessons and worked examplesChange one input
Vary one number while holding the others steady. This makes proportional, squared, and inverse relationships easier to recognize.
Read the steps
The worked substitution shows how the formula becomes a result. Compare it with your own setup before moving to the next problem.
Are the results saved?
Recent runs and practice progress are saved locally in this browser. No account is required, and the current calculator does not send those values to a server.
Can I use it for homework?
Yes, as a study companion. Use the steps and model to understand the setup, then verify the answer with your class materials or instructor.