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Projectile Motion Calculator

Physics

Calculate projectile motion instantly — enter initial velocity and launch angle to get max height, time of flight, and horizontal range, with a trajectory diagram.

Initial Velocity (m/s)
Launch Angle (°)

45° gives the maximum range for a given launch speed on level ground.

0 m0 m0 m45°

Horizontal Range

0 m

Max Height

0 m

Time of Flight

0 s

What is a Projectile Motion?

The Projectile Motion Calculator applies standard kinematics equations to compute the full trajectory of a launched object — its maximum height, time of flight, and horizontal range — from just an initial velocity and launch angle. It assumes standard Earth gravity (9.8 m/s²) and no air resistance, the same idealized model used in introductory physics.

Enter an initial velocity and a launch angle, and the calculator instantly returns all three key trajectory outputs along with a visual diagram showing the parabolic path, launch point, peak, and landing point.

If you need the launch velocity's associated energy, use the Kinetic Energy Calculator; for purely vertical motion without a launch angle, use the Free Fall Calculator instead.

How to use this Projectile Motion calculator

  1. Enter the initial velocity — the launch speed of the projectile, in meters per second.

  2. Enter the launch angle — the angle above the horizontal at which the projectile is launched, in degrees (0–90°).

  3. Read the range result — the highlighted result shows the horizontal range in meters.

  4. Check maximum height and time of flight — the two secondary results show the peak height and total flight duration.

  5. View the trajectory diagram — the diagram visualizes the parabolic path, launch point, peak, and landing point based on your inputs.

  6. Adjust the angle to explore range vs. height tradeoffs — try 45° for maximum range, or higher angles to see height increase at the cost of range.

Formula & Methodology

Component velocities:
vₓ = v × cos(θ), v_y = v × sin(θ)

Time of flight:
t = 2 × v_y ÷ g

Maximum height:
h = v_y² ÷ (2 × g)

Horizontal range:
R = vₓ × t

Variable definitions:
- v — initial velocity (meters per second)
- θ — launch angle (degrees)
- g — gravitational acceleration, fixed at 9.8 m/s²
- t — time of flight (seconds)
- h — maximum height (meters)
- R — horizontal range (meters)

Worked example:

A projectile is launched at 25 m/s at a 40° angle.

Step 1 — Component velocities: vₓ = 25 × cos(40°) ≈ 19.15 m/s, v_y = 25 × sin(40°) ≈ 16.07 m/s

Step 2 — Time of flight: t = 2 × 16.07 ÷ 9.8 ≈ 3.28 s

Step 3 — Maximum height: h = 16.07² ÷ (2 × 9.8) ≈ 13.19 m

Step 4 — Horizontal range: R = 19.15 × 3.28 ≈ 62.8 m

Note: This calculator assumes launch and landing occur at the same height and ignores air resistance. Real-world trajectories affected by drag, wind, or spin (such as a curveball) will deviate from these idealized results.

Frequently Asked Questions

This calculator uses standard projectile motion equations assuming no air resistance: time of flight = 2v·sin(θ)/g, maximum height = v²·sin²(θ)/(2g), and horizontal range = v²·sin(2θ)/g, where v is initial velocity, θ is launch angle, and g is gravitational acceleration (9.8 m/s²).
For a projectile launched and landing at the same height, 45° gives the maximum horizontal range for any given launch velocity. Angles above or below 45° (like 30° or 60°) produce equal ranges to each other but less than the 45° maximum, while affecting time of flight and maximum height differently.
No — this calculator uses idealized projectile motion equations that ignore air resistance (drag), which is the standard simplification used in introductory physics. Real-world projectiles, especially lightweight or high-speed ones, experience some deceleration from air resistance that these equations don't capture.
The standard equations used here assume launch and landing occur at the same vertical height (like a ball thrown and caught at the same level), which is the most common textbook scenario. If launch and landing heights differ, the time of flight and range calculations require additional terms not included in this simplified model.
Maximum height increases as the launch angle increases toward 90° (straight up), since more of the initial velocity is directed vertically. At 90°, the projectile has no horizontal range at all (it goes straight up and comes straight back down), while at 0° it has no height gain (it moves purely horizontally).
Time of flight increases as the launch angle increases, because a steeper angle sends more of the initial velocity into the vertical component, which takes longer to fall back down under gravity. A projectile launched straight up (90°) has the longest possible flight time for a given velocity, though it has zero range.
Use the [Kinetic Energy Calculator](/kinetic-energy-calculator/) with the projectile's mass and its initial velocity (the value you enter here) to find its kinetic energy at launch — useful for understanding the energy requirements of a given projectile motion scenario.
This calculator is commonly used for physics homework involving thrown or launched objects (balls, projectiles, water from a hose), estimating the range of sports equipment (like a kicked or thrown ball), and basic ballistics or engineering estimates where air resistance can be reasonably ignored.
This calculator uses Earth's standard gravitational acceleration of 9.8 m/s². A lower gravity (like the Moon's 1.62 m/s²) would produce a much longer time of flight, greater maximum height, and greater range for the same launch velocity and angle, since less force pulls the projectile back down.
The trajectory diagram plots a parabolic path using the calculated maximum height and horizontal range, showing the launch point, peak height, and landing point to scale — giving a quick visual sense of the projectile's path in addition to the exact numeric outputs.
The [Free Fall Calculator](/free-fall-calculator/) handles purely vertical motion starting from rest (like dropping an object), while this Projectile Motion Calculator handles motion with both horizontal and vertical velocity components from a launch angle — producing range and trajectory shape in addition to fall time.
No — launch angles are limited to between 0° and 90°, since these represent all physically meaningful directions of upward-and-forward motion for a projectile launched from ground level. Angles beyond 90° would represent launching backward or downward, which fall outside this calculator's standard forward-projectile model.
Also known as
trajectory calculatorrange of projectile calculatorlaunch angle calculatorprojectile range and height calculatortime of flight calculator