Enter your projectile's initial velocity, launch angle, and initial height to plot its complete flight path. The Trajectory Calculator returns maximum height, total range, and time of flight, plus a parabolic chart showing the full arc from launch to landing.
Total Horizontal Range
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Maximum Height
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Time of Flight
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Horizontal Velocity (Vx)
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Initial Vertical Velocity (Vy)
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A trajectory, also called a flight path, is the curved path a projectile follows under the influence of gravity. For objects launched near Earth's surface over short distances, the trajectory takes the shape of a parabola. The exact shape depends on the launch angle, initial speed, and initial height.
When launched from ground level (initial height = 0), a 45° angle produces the maximum horizontal range. However, if the projectile is launched from an elevated position, the optimal angle for maximum range is slightly less than 45°. You can experiment with the angle slider in this calculator to find the maximum range for your specific conditions.
At 30° and 10 m/s from ground level, the horizontal velocity component is about 8.66 m/s and the vertical component is 5 m/s. The projectile reaches a maximum height of roughly 1.27 m, travels a total horizontal range of about 8.83 m, and stays airborne for approximately 1.02 seconds.
Maximum height is calculated using the formula: H = h + (Vy²) / (2g), where h is the initial height, Vy is the initial vertical velocity (v₀ × sin θ), and g is gravitational acceleration. For example, with θ = 40° and v₀ = 5 m/s at ground level, Vy ≈ 3.21 m/s and maximum height ≈ 0.53 m.
The trajectory of a projectile follows a parabolic shape, assuming no air resistance. This is because the horizontal motion is constant (uniform) while the vertical motion is uniformly accelerated downward by gravity, combining to form a symmetrical (or asymmetrical if launched from height) parabola.
Time of flight is found by solving the vertical position equation y = h + Vy×t − ½g×t² for t when y = 0 (ground level). This gives a quadratic equation with two solutions; the positive root is the total flight time. A higher launch angle or greater initial height increases the time of flight.
Yes — in reality, air drag slows both horizontal and vertical velocity, reducing the range and lowering the peak height compared to ideal calculations. This calculator uses the standard physics equations without air resistance, providing a theoretical baseline. Ballistic calculators (like those used for firearms) incorporate drag coefficients and ballistic coefficients for more precise real-world results.
Yes! The gravitational acceleration selector lets you choose Earth, Moon, Mars, or Jupiter. Changing gravity dramatically affects the trajectory — on the Moon (g ≈ 1.62 m/s²), a projectile travels roughly six times farther than on Earth for the same launch conditions.