Projectile Time of Flight Calculator
A projectile launched at an angle follows a parabolic path under gravity alone, ignoring air resistance. From the launch speed, the angle above horizontal, and the starting height, you can find how long it stays in the air, how far it travels horizontally, and the peak height it reaches. This calculator solves the ideal kinematic equations with an editable gravitational acceleration, so it works for Earth or any other body, and returns the time of flight, the horizontal range, and the maximum height.
Projectile motion formula
vx = v * cos(theta); vy = v * sin(theta)
Time of flight t = (vy + sqrt(vy^2 + 2 g h)) / g
Horizontal range = vx * t
Maximum height = h + vy^2 / (2 g)
The angle is converted from degrees to radians. The time of flight is the positive root of the vertical position landing at ground level. Horizontal velocity stays constant, so range is simply horizontal speed times flight time.
Projectile motion facts
- From ground level, 45 degrees gives the maximum range with no air resistance.
- Horizontal and vertical motions are independent.
- The trajectory is a parabola when gravity is the only force.
- Launching from a height extends the flight time and range.
- Standard gravity is defined as 9.80665 metres per second squared.
Projectile time of flight: frequently asked questions
How is projectile time of flight calculated?
With launch speed v at angle theta from height h, the vertical motion gives time of flight t = (v sin theta + sqrt((v sin theta)^2 + 2 g h)) divided by g, where g is gravitational acceleration. This is the positive root of the vertical position equation set to zero (ground level).
What is the horizontal range?
The horizontal range equals the horizontal velocity times the time of flight: v cos theta times t. Because the horizontal velocity is constant (ignoring air resistance), once you know the flight time the range follows directly.
What value of gravity should I use?
Standard gravity at the Earth's surface is 9.80665 metres per second squared, which is the value defined by international standards. This calculator exposes g as an editable input so you can use a local value or model another body such as the Moon (about 1.62) or Mars (about 3.71).
Does this calculator include air resistance?
No. These are the ideal projectile formulas with no drag, valid for dense, slow, or short-range projectiles. Real trajectories with significant air resistance fall short of the ideal range and have a shorter, asymmetric flight, which requires numerical modelling.
What launch angle gives the maximum range?
From ground level with no air resistance, 45 degrees gives the maximum range. When launched from a height above the landing point, the optimal angle is slightly less than 45 degrees. This calculator computes the range for whatever angle you enter.
Official sources
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.