What this parabolic motion calculator does
This parabolic motion calculator helps you analyze projectile motion in seconds. Enter an initial speed, launch angle, starting height, and gravity value, and it computes the core kinematics results: time of flight, horizontal range, peak height, launch components, and impact conditions.
It is useful for physics students, educators, athletes, and engineers who want a quick way to understand trajectory behavior without solving equations manually each time.
Core projectile motion equations used
Horizontal motion
Horizontal velocity stays constant (ignoring drag):
vx = v0 cos(θ)
x(t) = vx t
Vertical motion
Vertical position changes with constant downward acceleration:
vy = v0 sin(θ)
y(t) = h0 + vy t - ½ g t²
- Time to peak:
tpeak = vy/g - Maximum height:
hmax = h0 + vy²/(2g) - Flight time: positive root of
h0 + vyt - ½gt² = 0 - Range:
R = vx tflight
How to use this calculator
- Enter the initial speed in meters per second.
- Enter the launch angle in degrees (0° to 90°).
- Set initial height to 0 for ground launches, or a positive value for elevated launches.
- Use 9.81 m/s² for Earth unless you are modeling another planet.
- Click Calculate to view results, sample points, and a trajectory plot.
Example interpretation
Suppose a ball is launched at 25 m/s, angle 40°, from 1.5 m height. The calculator breaks the motion into horizontal and vertical parts, then reports how high it goes, how long it stays airborne, and where it lands. This makes it easier to compare setups like “faster speed at lower angle” vs “slower speed at higher angle.”
Angle and speed insights
- Increasing speed generally increases both range and peak height.
- At the same launch and landing height, range is typically maximized near 45°.
- Higher angles give more airtime and height, but not always maximum distance.
- Launching from a higher platform increases total flight time and range.
Common mistakes to avoid
- Mixing units (for example, km/h for speed with meters for distance).
- Using angle from the vertical instead of from the horizontal.
- Forgetting that this model ignores air resistance and wind.
- Using negative gravity or impossible input combinations.
FAQ
Does this include air drag?
No. This is the classic ideal projectile model with no drag.
Can I use this for sports trajectories?
Yes, as a first approximation. For realistic balls (soccer, baseball, golf), drag and spin can significantly change the path, especially at high speeds.
Can I change gravity for the Moon or Mars?
Absolutely. Enter the local gravity value to estimate projectile behavior in different environments.