Projectile Motion Calculator
This projectile motion calculator finds the range, maximum height, and flight time of a projectile from its launch speed and angle. Enter them and the projectile motion calculator returns all three. As a projectile motion solver it uses the standard equations with no air resistance, so it fits physics problems and quick estimates.
Results
The Projectile Motion Calculator is part of our Motion & Force collection. Browse more motion & force to size, convert, and check your work alongside this tool.
What the projectile motion calculator shows
A projectile launched at an angle follows a curved path set by its speed, its angle, and gravity. This projectile motion calculator splits the launch into horizontal and vertical parts and returns the range, the maximum height, and the time in the air. As a projectile motion solver it handles any launch angle from flat to straight up, ignoring air resistance.
How the projectile motion solver works
The projectile motion solver splits the launch speed into a horizontal part and a vertical part, then applies the range, height, and time equations:
v is the launch speed, θ is the angle, and g is gravity. The range peaks at 45 degrees, while a steeper angle trades range for height. These are the standard projectile motion formula calculator equations, with no air resistance.
Projectile range calculator example
A launch at 20 m/s and 45 degrees on Earth. The projectile range calculator gives:
The flight time is about 2.88 seconds. Change the angle and the projectile motion calculator updates all three at once.
How to use the projectile motion calculator
Enter the initial velocity in metres per second, the launch angle in degrees, and the gravity value, then the projectile motion calculator returns the range, the maximum height, and the flight time. Use 45 degrees for the longest range at a given speed. The projectile is assumed to launch and land at the same height, which is the standard case a projectile calculator solves.
Reading the projectile motion calculator result
The range is how far the projectile travels horizontally, the maximum height is the top of its arc, and the flight time is how long it stays in the air. At a fixed speed, 45 degrees gives the longest range; angles either side of it give the same range as their complement, so 30 and 60 degrees match. A steeper launch flies higher but not as far. These results ignore air resistance, so a real ball or arrow falls short of the projectile calculator range, more so at high speed.
When to use the projectile calculator
- Solving physics homework with the projectile calculator
- Finding the range and height of a launch
- Checking answers with a projectile motion problem solver
- Comparing launch angles for maximum range
Common projectile motion calculator mistakes
- Using degrees as radians. Enter the angle in degrees; the projectile calculator converts it.
- Expecting air resistance. These are ideal results; a real projectile falls short.
- Forgetting the complement. Angles either side of 45 degrees give the same range, so 30 and 60 match.
Tips for projectile problems
- Use 45 degrees for the maximum range at a given speed.
- Split the launch into horizontal and vertical parts.
- Remember the results ignore air resistance.
Horizontal projectile motion calculator
A horizontal projectile motion calculator covers the case where an object is launched flat from a height, like a ball rolled off a table. The horizontal speed stays constant because nothing slows it sideways, while the vertical motion is pure free fall, so the object falls the same way it would if simply dropped. The time in the air comes from the height, and the range is that time times the horizontal speed. This is why a bullet fired flat and a bullet dropped from the same height hit the ground together: the vertical motion is identical. Splitting a launch into a steady horizontal part and a free fall vertical part is the key idea a projectile trajectory calculator uses for any angle.
Projectile trajectory calculator and problem solver
The full path, or trajectory, is a parabola, and a projectile trajectory calculator traces it by stepping the horizontal and vertical positions over time. A projectile motion problem solver works the same equations backward too: given a range and angle it finds the speed, or given a target height it finds the launch. The three headline numbers, range, maximum height, and flight time, come straight from the launch speed and angle, so once you have those the whole arc is set. Real projectiles feel air drag, which shortens the range and lowers the peak, but for dense objects over short distances the no drag result from this projectile motion calculator is close. The acceleration calculator covers the general accelerated motion these equations are built from.
Projectile motion calculator values by angle
Range, height, and time at 20 m/s for several launch angles, from the projectile motion calculator:
| Angle | Range | Max height | Flight time |
|---|---|---|---|
| 15° | 20.4 m | 1.4 m | 1.06 s |
| 30° | 35.3 m | 5.1 m | 2.04 s |
| 45° | 40.8 m | 10.2 m | 2.88 s |
| 60° | 35.3 m | 15.3 m | 3.53 s |
Projectile Motion Calculator FAQ
What angle gives the longest range?
Forty five degrees gives the longest range at a given speed. Angles either side give the same range as their complement, so 30 and 60 degrees match.
What is the projectile range formula?
Range = v squared times sin(2 theta) divided by g. The projectile motion calculator applies it along with the height and time equations.
Does this include air resistance?
No. This is ideal projectile motion. A real ball or arrow falls short of the projectile calculator range, more so at high speed.
Can it solve horizontal launches?
Yes. A horizontal projectile motion calculator is the special case of a zero degree launch from a height, where the range depends on the drop and the speed.