Projectile Motion Calculator
Calculate range, flight time, and max height from launch speed and angle.
Check Projectile Motion Calculator
Trajectory breakdown
Projectile motion becomes easier when you separate horizontal motion from vertical motion before interpreting the result.
Horizontal and vertical components drive different parts of the motion.
- 1Resolve launch speed into components: vx = 18.3851 m/s and vy = 15.4269 m/s.
- 2Use the vertical motion and gravity to determine the total flight time: 3.1462 s.
- 3Use horizontal motion for range: x = vx * t = 18.3851 * 3.1462.
- 4Peak height follows from the vertical energy balance: 12.1341 m.
Projected path
This is a scaled preview of the ideal trajectory for the current launch inputs.
The curve is idealized: no drag, no wind, and constant gravity across the whole flight.
Formula result
Check before you use it
What the numbers show
The answer breaks launch motion into horizontal and vertical parts so flight time, range, peak height, and component speeds can be interpreted together.
Use projectile motion calculator for ball toss labs, sports launch estimates, classroom trajectory problems, range comparisons, and launch-angle exploration.
Small changes in launch angle can shift range and maximum height in different directions.
Copy-ready formula handoff
Use this after solving the live calculator result, then paste the answer into a lab note, homework check, or engineering review.
v_x = v0*cos(theta), v_y = v0*sin(theta), t = (v_y + sqrt(v_y^2 + 2*g*h0)) / g, range = v_x*t
- Launch speed: Initial speed at launch before splitting into horizontal and vertical components.
- Launch angle: Angle above the horizontal at the launch point.
- Initial height: Starting height above the landing level, such as a platform or release height.
- Gravity: Constant downward gravitational acceleration for the selected location.
- Air resistance and wind are ignored.
- Gravity is treated as constant over the trajectory.
- Using degrees in a calculator or spreadsheet function that expects radians for sin and cos.
- Solving range before flight time; vertical motion determines how long horizontal motion lasts.
Projectile Motion Calculator result: [paste the solved value from the calculator above]. Formula used: v_x = v0*cos(theta), v_y = v0*sin(theta), t = (v_y + sqrt(v_y^2 + 2*g*h0)) / g, range = v_x*t Inputs checked: Launch speed, Launch angle, Initial height, Gravity. Assumptions: Air resistance and wind are ignored. Gravity is treated as constant over the trajectory. Worked example: Ball launched at 18 m/s and 35 degrees from a 1.2 m platform. Resolve components: vx = 18*cos(35 deg) = 14.74 m/s and vy = 18*sin(35 deg) = 10.32 m/s. With h0 = 1.2 m and g = 9.80665 m/s^2, flight time is about 2.22 s. Range = 14.74 * 2.22 = 32.67 m, and maximum height above the landing level is about 6.63 m. Next check: Using degrees in a calculator or spreadsheet function that expects radians for sin and cos.
Equation context
Built for ball toss labs, sports launch estimates, classroom trajectory problems, range comparisons, and launch-angle exploration. This page pairs the live calculator with the governing formula, variable glossary, and a worked example so the result is easier to trust and reuse.
Quick entry points
Use the calculator to verify arithmetic after you set up the formula yourself.
Change one input at a time to see which variable is driving the result.
Review the formula notes before using the answer in a lab or design check.
Variables to track
Initial speed at launch before splitting into horizontal and vertical components. Unit: m/s.
Angle above the horizontal at the launch point. Unit: deg.
Starting height above the landing level, such as a platform or release height. Unit: m.
Constant downward gravitational acceleration for the selected location. Unit: m/s^2.
Time from launch until the ideal path reaches the landing level. Unit: s.
Horizontal distance traveled during the flight time. Unit: m.
Formula method and unit assumptions
Formula and example
Worked example
Ball launched at 18 m/s and 35 degrees from a 1.2 m platform
- 1Resolve components: vx = 18*cos(35 deg) = 14.74 m/s and vy = 18*sin(35 deg) = 10.32 m/s.
- 2With h0 = 1.2 m and g = 9.80665 m/s^2, flight time is about 2.22 s.
- 3Range = 14.74 * 2.22 = 32.67 m, and maximum height above the landing level is about 6.63 m.
The vertical equation sets the time in the air; the horizontal equation then turns that time into range.
Assumptions
Common mistakes
Related formula checks
Equation context and next checks
Formula and variable setup for Projectile Motion Calculator
Calculate range, flight time, and max height from launch speed and angle. The page is designed to help you move from the known values to the correct formula without rebuilding the derivation every time.
For projectile motion calculator, the safest workflow is to confirm the unit system first, then map each symbol to the physical quantity in your problem statement before solving.
- v0: Launch speed (m/s) - Initial speed at launch before splitting into horizontal and vertical components.
- theta: Launch angle (deg) - Angle above the horizontal at the launch point.
- h0: Initial height (m) - Starting height above the landing level, such as a platform or release height.
- g: Gravity (m/s^2) - Constant downward gravitational acceleration for the selected location.
- t: Flight time (s) - Time from launch until the ideal path reaches the landing level.
- range: Horizontal range (m) - Horizontal distance traveled during the flight time.
How to read the result
The answer breaks launch motion into horizontal and vertical parts so flight time, range, peak height, and component speeds can be interpreted together.
This tool is especially useful for ball toss labs, sports launch estimates, classroom trajectory problems, range comparisons, and launch-angle exploration. The output becomes more trustworthy when you compare nearby cases instead of relying on one single run.
- Range and flight time
- Maximum height
- Initial height support
Assumptions and limits
The calculator applies the standard textbook relation for this topic, which makes it a strong first-pass answer but not always a full real-world model.
Before you use the result in a lab, design review, or report, check whether the simplified assumptions still match the physical system you care about.
- Air resistance and wind are ignored.
- Gravity is treated as constant over the trajectory.
- The result is a clean ideal trajectory, not a full real-world ballistics model.
- Launch and landing are assumed to happen in one vertical plane with no sideways spin or lift.
Quick glossary
Initial speed at launch before splitting into horizontal and vertical components.
Angle above the horizontal at the launch point.
Starting height above the landing level, such as a platform or release height.
A simplified physics model that omits secondary effects so the first-order relationship is easier to inspect.
Formula checks before using the result
Formula questions
Checks before using the result
When should I use the projectile motion calculator?
Use projectile motion calculator for ball toss labs, sports launch estimates, classroom trajectory problems, range comparisons, and launch-angle exploration, especially when the governing formula is already known and the main need is a fast, transparent calculation.
What is the main thing the projectile motion calculator tells me?
The answer breaks launch motion into horizontal and vertical parts so flight time, range, peak height, and component speeds can be interpreted together.
What can make the projectile motion calculator answer inaccurate?
The answer is exact for the formula and assumptions on the page, but it can drift when the real system violates those assumptions. Common limits include Air resistance and wind are ignored. Gravity is treated as constant over the trajectory. The result is a clean ideal trajectory, not a full real-world ballistics model. Launch and landing are assumed to happen in one vertical plane with no sideways spin or lift.
Formula references and related examples
Formula Basis