Projectile Motion Calculator
Calculate every property of a projectile's trajectory online for free. Enter initial velocity, launch angle, and optional initial height to instantly get horizontal range, maximum height, time of flight, impact velocity, and impact angle — with a live trajectory graph and full formula reference. Fast, private, and no signup required.
Enter the initial velocity, launch angle, and optional initial height to calculate range, maximum height, time of flight, and impact velocity. All calculations use standard gravity (g = 9.80665 m/s²) and run locally in your browser — no signup required.
Speed at launch (m/s)
0° = horizontal, 90° = vertical
Height above ground at launch
Why Use Our Projectile Motion Calculator?
Instant Projectile Motion Calculator Online
Enter initial velocity, launch angle, and optional height to instantly compute range, maximum height, time of flight, impact velocity, and impact angle. The projectile motion calculator handles any realistic launch scenario — from sports throws to cliff launches — in milliseconds.
Secure Projectile Motion Calculator — 100% Private
The projectile motion calculator runs entirely client-side in your browser. Your inputs are never uploaded to any server, stored, or tracked — completely private for academic, engineering, or physics coursework.
Projectile Motion Calculator Online — No Installation
Use the projectile motion calculator directly in any modern browser with no downloads, apps, or plugins required. Works on desktop, tablet, and mobile — 100% free forever with no signup required.
Live Trajectory Graph & Full Formula Reference
The projectile motion calculator renders a live SVG trajectory graph showing the parabolic path, peak height, launch point, and landing point. All formulas used — including velocity components, time of flight, and range — are displayed alongside results for easy verification.
Common Use Cases for Projectile Motion Calculator
Physics Homework & Exams
Students use the projectile motion calculator to verify homework answers for range, maximum height, and time of flight. The projectile motion calculator shows all formulas alongside results, making it easy to understand the derivation and check work step by step.
Sports Science & Biomechanics
Coaches and sports scientists use the projectile motion calculator to analyse ball trajectories in football, basketball, javelin, and shot put. Optimising the launch angle with the projectile motion calculator helps athletes maximise range or height for their event.
Engineering & Ballistics
Engineers use the projectile motion calculator to model the trajectory of launched objects in mechanical systems, robotics, and defence applications. The range and impact velocity outputs are essential for safety clearance and target accuracy calculations.
Game Development & Simulation
Game developers use the projectile motion calculator to tune realistic physics for thrown objects, grenades, and arrows. The trajectory graph and time-of-flight output help calibrate in-game physics engines to match real-world behaviour.
Cliff & Elevated Launch Scenarios
The projectile motion calculator supports a non-zero initial height, making it ideal for modelling launches from cliffs, buildings, or elevated platforms. The extended time of flight and increased range compared to ground-level launches are computed automatically.
Teaching & Classroom Demonstrations
Teachers use the projectile motion calculator to demonstrate how launch angle affects range and height in real time. The live trajectory graph makes it easy to show students why 45° maximises range on flat ground and how initial height changes the optimal angle.
Understanding the Projectile Motion Calculator
What is a Projectile Motion Calculator?
A projectile motion calculator is a tool that computes the trajectory of an object launched into the air under the influence of gravity alone — with no air resistance. Our online projectile motion calculator takes the initial velocity, launch angle, and optional initial height as inputs and instantly outputs the horizontal range, maximum height, time of flight, impact velocity, and impact angle. It also renders a live trajectory graph showing the full parabolic path. The projectile motion calculator uses standard gravity g = 9.80665 m/s² and runs entirely in your browser — no signup required.
How Our Projectile Motion Calculator Works
- Enter Initial Velocity and Launch Angle: Type the launch speed in metres per second and the angle above horizontal in degrees (0° = horizontal, 90° = straight up). The projectile motion calculator decomposes the velocity into horizontal (v₀ₓ = v₀ · cos θ) and vertical (v₀ᵧ = v₀ · sin θ) components.
- Optionally Enter Initial Height:If the projectile is launched from an elevated position — a cliff, platform, or building — enter the height above the landing surface. The projectile motion calculator solves the full quadratic equation for time of flight when h₀ > 0.
- Review Results and Trajectory Graph: The projectile motion calculator displays all outputs in grouped stat cards with the formula used for each, renders a live SVG trajectory graph, and provides a copy-to-clipboard summary of all results.
Key Projectile Motion Formulas
- Velocity Components: v₀ₓ = v₀ · cos(θ) and v₀ᵧ = v₀ · sin(θ) — the horizontal component stays constant throughout the flight; the vertical component decreases at rate g.
- Position Equations: x(t) = v₀ₓ · t and y(t) = h₀ + v₀ᵧ · t − ½g · t² — these parametric equations define the parabolic trajectory.
- Time of Flight: Solved from y(T) = 0 using the quadratic formula: T = (v₀ᵧ + √(v₀ᵧ² + 2g·h₀)) / g. For h₀ = 0 this simplifies to T = 2v₀ᵧ / g.
- Maximum Height: H_max = h₀ + v₀ᵧ² / (2g) — reached at time t_peak = v₀ᵧ / g when the vertical velocity equals zero.
- Horizontal Range: R = v₀ₓ · T — the total horizontal distance travelled. For h₀ = 0, this simplifies to R = v₀² · sin(2θ) / g, which is maximised at θ = 45°.
- Impact Velocity: v_impact = √(v₀ₓ² + vᵧ(T)²) where vᵧ(T) = v₀ᵧ − g·T. By conservation of energy, impact speed equals launch speed when h₀ = 0.
Assumptions and Limitations
The projectile motion calculator assumes no air resistance (drag), a flat Earth surface, and constant gravitational acceleration of 9.80665 m/s². In real-world scenarios, air resistance significantly reduces range and maximum height for high-speed projectiles. The projectile motion calculator is ideal for introductory physics, sports science, and engineering estimates where drag is negligible or a first-order approximation is sufficient.
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Frequently Asked Questions About Projectile Motion Calculator
A projectile motion calculator computes the trajectory of an object launched at an angle under gravity — with no air resistance. Our online projectile motion calculator takes initial velocity, launch angle, and optional initial height and instantly outputs range, maximum height, time of flight, impact velocity, and impact angle. It runs entirely in your browser with no signup required.
For a projectile launched from and landing at the same height (h₀ = 0), a launch angle of 45° gives the maximum horizontal range. When the initial height is greater than zero, the optimal angle for maximum range is slightly less than 45°. The projectile motion calculator lets you experiment with different angles to see how range changes.
A non-zero initial height increases both the time of flight and the horizontal range, because the projectile has extra vertical distance to fall before hitting the ground. The projectile motion calculator solves the full quadratic equation y(t) = 0 to find the correct time of flight when h₀ > 0, rather than using the simplified flat-ground formula.
No — the projectile motion calculator assumes no air resistance (drag). In reality, air resistance reduces range and maximum height, especially for high-speed or low-density projectiles. The calculator provides the ideal theoretical trajectory, which is accurate for dense, slow-moving objects and is the standard model used in introductory physics.
Yes. The projectile motion calculator runs 100% locally in your browser. Your inputs are never sent to any server, stored, or tracked in any way — completely private for academic, engineering, or classroom use.
Yes — the projectile motion calculator is 100% free with no signup, no account, and no usage limits. Use it as many times as you need, completely free forever.
By conservation of energy, a projectile launched and landing at the same height has the same kinetic energy at both points, so its speed is identical. The direction changes — the impact angle below horizontal equals the launch angle above horizontal — but the magnitude of velocity is preserved. The projectile motion calculator confirms this with its impact velocity output.
The time of flight T is found by solving y(T) = h₀ + v₀ᵧ·T − ½g·T² = 0 using the quadratic formula: T = (v₀ᵧ + √(v₀ᵧ² + 2g·h₀)) / g. For h₀ = 0 this simplifies to T = 2v₀ᵧ / g = 2v₀·sin(θ) / g. The projectile motion calculator uses the full quadratic form to support elevated launches.
Yes. At 90°, the horizontal velocity component is zero, so the range is 0 and the projectile goes straight up and comes straight back down. The projectile motion calculator correctly handles this edge case — the time of flight is 2v₀/g and the maximum height is v₀²/(2g) above the launch point.