Physics
Projectile Graph Calculator
Resolve launch velocity, evaluate exact horizontal and vertical position at the selected time, and mark the apex and level-ground range reference.
Horizontal velocity (m/s)-
Vertical velocity (m/s)-
Horizontal position at sample time (m)-
Vertical position at sample time (m)-
Time to apex (s)-
Maximum height (m)-
Level-ground flight-time reference (s)-
Level-ground range reference (m)-
Decision view
Ideal projectile trajectory and sample point
Ideal projectile trajectory and sample pointHorizontal and vertical velocity determine the exact x-y position at the selected sample time.
Exact scenario comparisonTrajectory sample time (seconds) changes while all other entered assumptions remain constant.
| Trajectory sample time (seconds) | Horizontal velocity (m/s) | Vertical velocity (m/s) | Horizontal position at sample time (m) | Vertical position at sample time (m) | Time to apex (s) | Maximum height (m) | Level-ground flight-time reference (s) | Level-ground range reference (m) |
|---|
How to use Projectile Graph Calculator
- Confirm launch speed, angle, height, and gravity.
- Choose a sample time inside the physically relevant flight.
- Treat below-ground mathematical points as outside the modeled flight.
Calculator guide
Understanding Projectile Graph Calculator
A projectile graph is a time-parameterized ideal trajectory, not a generic line between launch and landing.
Calculation method
How the calculation works
Evaluate the ideal projectile equations at an exact sample time and expose component velocities, position, apex, and a level-ground range reference for graphing. Use x(t)=vₓt and y(t)=h₀+vᵧt−½gt², with apex time vᵧ/g and a separate level-ground reference based on the simplified symmetric-flight expression.
Graph reading
Identify the four useful landmarks
Each marker answers a different question.
Worked situations
Practical examples
- Horizontal position grows linearly without drag.
- Vertical position follows a parabola.
- The level-ground range reference does not incorporate elevated launch height.
Better inputs
Useful tips
- Mark impact using a root-solving model when launch height matters.
- Use measured gravity only when necessary.
- Add drag for real ballistic prediction.
Before relying on the result
Limitations and common mistakes
- Drag, wind, spin, lift, terrain, launcher geometry, uncertainty, and safety are excluded.
- The level-flight reference assumes a simplified landing level.
- A sample after impact remains a mathematical value only.
Reference
Key terms
- Parametric trajectory
- Position described as x and y functions of time.
- Sample point
- Calculated position at the entered time.
- Apex
- Highest ideal point.
- Level-ground range
- Simplified horizontal distance for equal launch and landing levels.
Important note
Calculated from the entered values using the displayed physical model. Confirm that its assumptions, units, boundary conditions, and safety limits match the application.
Frequently asked questions
Why can sample height be negative?
The equation continues mathematically after the projectile would have crossed the landing level.
Does the range use initial height?
The displayed level-ground reference does not.
Is the path safe to use operationally?
No.
Does mass affect the ideal path?
Not in this drag-free model.