Why does 45° give the maximum range on flat ground?

At 45° the horizontal and vertical velocity components are equal. Any steeper angle sends more energy upward (wasted in height), while any shallower angle reduces air time before gravity pulls the projectile down. The 45° sweet spot maximizes the product of horizontal speed and time aloft.

Does air resistance affect real bullets?

Yes, significantly. This tool uses vacuum physics (no drag), so the computed range will be higher than actual bullet drop at long distances. For precision long-range shooting, use a ballistic coefficient (BC) calculator that accounts for atmospheric drag. This tool is best for approximate estimates and education.

How does height difference change the optimal angle?

When shooting downhill the optimal angle for maximum range is slightly less than 45°; shooting uphill it is slightly above 45°. The calculator shows the actual result for whatever angle you input — just adjust and compare.

What units should I use for hunting rifle data?

Most US ballistic data is listed in fps (feet per second). Select Imperial units and enter your muzzle velocity from the ammo box. Metric users can switch to m/s — 1 fps ≈ 0.305 m/s.

Can I use this for archery or airsoft?

Yes. Enter the arrow speed in fps (typically 250–350 fps for compound bows) and the launch angle. The physics is identical; only the specific numbers differ.

Ballistic Trajectory Calculator

Name: Ballistic Trajectory Calculator
Availability: InStock
Author: Nham Vu

Enter muzzle velocity, launch angle, and optional height offset to calculate a projectile's range, maximum height, and time of flight.

Launch Parameters

Muzzle Velocity (fps)

Typical rifle: 2500–3500 fps. Bow: 250–350 fps.

Launch Angle (degrees, 0–90)

0° = flat; 45° = maximum range on level ground.

Height Difference (ft, optional)

Positive = target above shooter. Negative = target below.

Angle vs. Range (level ground)

Enter a velocity above to populate this table.

Angle	Range	Max Height
—

Summary

Enter muzzle velocity, launch angle, and optional height offset to calculate a projectile's range, maximum height, and time of flight.

How it works

Enter the muzzle velocity in feet per second (fps) or meters per second (m/s).
Enter the launch angle in degrees above horizontal (0° = flat, 45° = maximum range).
Optionally enter a height difference: positive if the target is above the shooter, negative if below.
Click Calculate to get the horizontal range, maximum height above the launch point, and total time of flight.
Switch between Imperial (ft, fps) and Metric (m, m/s) units as needed.
Use the trajectory chart to visualize the arc of the projectile.

Use cases

Estimating bullet drop and range for long-range rifle shooting.
Planning shots at uphill or downhill targets while hunting.
Teaching projectile motion physics with real shooting scenarios.
Comparing trajectories at different launch angles for the same muzzle velocity.
Checking arrow or slug flight time for moving-target lead estimates.
Verifying ballistics app outputs with a simple physics baseline.

Frequently Asked Questions

Last updated: 2026-07-01 · Reviewed by Nham Vu