Input Parameters
| Distance (m) | Height (m) | Drop from muzzle (m) | Time (s) | Vertical velocity (m/s) | Speed (m/s) | Energy (J) | Wind drift (m) |
|---|
Table stops once the projectile reaches ground level or the maximum distance.
Example Ballistic Trajectory Data
These examples show typical trajectories for common muzzle velocities and angles. Values assume gravity of 9.81 m/s² and no air resistance.
| Velocity (m/s) | Angle (°) | Initial height (m) | Gravity (m/s²) | Time of flight (s) | Range (m) | Max height (m) |
|---|---|---|---|---|---|---|
| 820 | 5 | 1.5 | 9.81 | 14.7 | 11900 | 270 |
| 800 | 10 | 1.5 | 9.81 | 28.1 | 22200 | 990 |
| 700 | 15 | 1.5 | 9.81 | 39.1 | 26400 | 1650 |
Formulas Used in This Calculator
This calculator models ideal projectile motion, assuming a constant gravitational field and no aerodynamic drag.
The projectile is fired with initial speed v0 at an angle θ above the horizontal,
from an initial height h0.
-
Horizontal velocity:
vx = v0 · cos(θ) -
Initial vertical velocity:
vy0 = v0 · sin(θ) -
Horizontal position:
x(t) = vx · t -
Vertical position:
y(t) = h0 + vy0 · t - 0.5 · g · t² -
Time of flight (until the projectile reaches ground level,
y = 0):
tf = (vy0 + √(vy0² + 2 g h0)) / g -
Horizontal range:
R = vx · tf -
Maximum height above ground:
hmax = h0 + vy0² / (2 g) -
Vertical velocity at time
t:vy(t) = vy0 - g · t -
Resulting speed at time
t:v(t) = √(vx² + vy(t)²) -
Kinetic energy (using bullet mass
min kilograms):E(t) = 0.5 · m · v(t)² -
Simple full-value crosswind drift using crosswind speed
w:d(t) = w · t
Real bullets experience air drag, spin drift, and complex wind effects. This idealised model is useful for education, trends, and initial planning, not for safety-critical firing solutions.
How to Use This Ballistic Trajectory Calculator
- Enter the muzzle velocity from your firearm or ballistics chart in metres per second.
- Set the launch angle in degrees relative to the horizontal firing line.
- Specify the initial height of the barrel (or sight) above the ground level.
- Pick an environment preset or enable custom gravity, then confirm the gravity value in metres per second squared.
- Choose the maximum horizontal distance and a table stepping mode, using either distance steps or regular time steps for sampling.
- Optionally provide bullet mass in grams, target distance, and crosswind speed to estimate energy and lateral drift along the trajectory.
- Press Calculate Trajectory to generate the summary and table. Use Download CSV or Print / Save as PDF for exporting.
- Compare different scenarios by adjusting one variable at a time and saving exported results as part of your learning or planning notes.
Always verify trajectories with real-world testing and follow all safety rules when working with firearms or high-speed projectiles.
Ballistic Trajectory Concepts and Applications
Understanding ideal projectile motion
Ballistic trajectory models in this calculator are based on ideal projectile motion. The projectile experiences only constant gravitational acceleration, with air drag, spin drift, and complex atmospheric effects intentionally ignored. That simplification keeps the equations transparent while still capturing the main relationships between speed, angle, height, and impact point.
Role of muzzle velocity and launch angle
Muzzle velocity and launch angle largely determine range and maximum height. Higher velocity stretches the trajectory and increases energy delivery, while moderate launch angles usually provide flatter paths that are easier to zero with real optics. Exploring different combinations quickly reveals how small changes translate into dramatic differences downrange.
Importance of initial height above ground
Initial height represents the difference between muzzle, or sight line, and ground level. Even small height changes significantly alter impact point at distance, especially on shallow angles where the projectile spends longer time above the terrain. Hunters, competitors, and engineers often adjust this parameter to match realistic shooting platforms.
Gravity and environmental variations
Gravity controls how quickly vertical velocity decays and when the projectile returns to ground. This calculator allows custom gravitational acceleration, so you can explore trajectories on other planets, moons, or experimental microgravity environments. Students can compare results directly and see how altered gravity reshapes range, arc, and time aloft.
Using time of flight and range data
Time of flight values indicate how long the projectile remains airborne before impact. Combined with horizontal range, they help evaluate suitability of a shot or compare different loads. Longer flight times increase exposure to wind and motion, which becomes obvious when you examine the distance–time table rows.
Energy loss and terminal performance
When bullet mass is provided, the calculator estimates kinetic energy along the path. Although aerodynamic drag is not modeled, relative changes illustrate how impact energy evolves with distance and how launch parameters influence terminal performance. Comparing energies at different ranges supports preliminary decisions about acceptable shot distances.
Limitations and practical verification
This idealised model simplifies real-world ballistics, offering insight into trends rather than precise firing solutions. Always confirm predicted trajectories at a safe range, record actual impact points, and refine your settings. Treat the calculator as a teaching and planning aid, not a substitute for disciplined live-fire verification.
By adjusting inputs, exporting CSV tables, and printing PDF reports, users can document trajectories for future comparison. That workflow supports lesson plans, engineering notes, or range logs created from consistent, repeatable ballistic calculations generated with this trajectory tool.
Frequently Asked Questions
Can this calculator model trajectories in different gravity environments?
Yes. Change the gravity field, muzzle velocity, launch angle, or initial height to simulate different planets, reduced gravity environments, or experimental platforms without rewriting equations.
How is wind drift estimated in the results table?
Wind drift is estimated simply as crosswind speed multiplied by time of flight. It assumes a full-value, constant crosswind and ignores aerodynamic drag, turbulence, or shielding from terrain and vegetation.
Does the tool calculate kinetic energy at each distance?
Yes. When bullet mass is supplied, the calculator estimates kinetic energy at each distance row. Those values help compare loads or check whether a given range still meets your minimum impact energy requirements.
How should I use these results for real shooting adjustments?
Use the tool as a planning and teaching reference, then confirm predicted impacts on a safe range. Adjust sights or holdovers based on real groups, never solely on idealised calculator outputs.
Can I limit the table to specific distances only?
Yes. Use the distance step and maximum distance fields to limit the table. Export CSV results, filter rows in your spreadsheet, and keep only the ranges that matter for your application.
What are practical uses for the CSV and PDF exports?
Printed reports and CSV exports are useful for lesson plans, range notebooks, or engineering records. They keep raw calculations, trajectory shapes, and key numbers documented so you can repeat or compare scenarios later.