⏱️ Time of Flight Calculator – Projectile Motion
Calculate how long a projectile stays in the air
How to Use This Calculator
Enter Initial Velocity
Input the initial speed at which the projectile is launched, measured in meters per second (m/s). This is the magnitude of the velocity vector at launch.
Enter Launch Angle
Input the angle at which the projectile is launched above the horizontal, measured in degrees. This affects both the time of flight and the trajectory.
Enter Initial Height (Optional)
If the projectile starts from a height above ground level, enter that initial height in meters. Leave as 0 if launched from ground level. Higher initial height increases flight time.
Set Gravity (Optional)
The default gravity is 9.81 m/s² (Earth's gravity). You can change this value for calculations on other planets or in different gravitational fields.
Click Calculate
Press the "Calculate Time of Flight" button to compute the total time the projectile stays in the air, along with the time to reach maximum height and the range.
Formula
T = (v₀ sin(θ) + √(v₀² sin²(θ) + 2gh₀)) / g
Time to Max Height: t_max = v₀ sin(θ) / g
Where:
T = Time of flight (s)
v₀ = Initial velocity (m/s)
θ = Launch angle (degrees)
h₀ = Initial height (m)
g = Gravitational acceleration (m/s²)
v₀y = v₀ sin(θ) - vertical component of velocity
Example 1: Projectile from ground level at 45°
Given: v₀ = 30 m/s, θ = 45°, h₀ = 0 m, g = 9.81 m/s²
Step 1: Calculate vertical component
v₀y = 30 × sin(45°) = 30 × 0.707 = 21.21 m/s
Step 2: Calculate time of flight
T = (21.21 + √(21.21² + 0)) / 9.81
T = (21.21 + 21.21) / 9.81 = 42.42 / 9.81 = 4.32 s
Time to max height: t_max = 21.21 / 9.81 = 2.16 s (exactly half of total time)
Example 2: Projectile from elevated position
Given: v₀ = 25 m/s, θ = 60°, h₀ = 10 m, g = 9.81 m/s²
v₀y = 25 × sin(60°) = 21.65 m/s
T = (21.65 + √(21.65² + 2×9.81×10)) / 9.81
T = (21.65 + √(468.72 + 196.2)) / 9.81
T = (21.65 + √664.92) / 9.81 = (21.65 + 25.79) / 9.81 = 4.84 s
Note: Initial height increases flight time
Example 3: Understanding the formula
• For ground level (h₀ = 0): T = 2v₀ sin(θ) / g
• Time to max height is exactly half the total time (for symmetric trajectories)
• Maximum flight time occurs at 90° (vertical launch)
• At 45°, flight time is maximum for ground-level launches (same as maximum range)
About Time of Flight Calculator – Projectile Motion
The Time of Flight Calculator for Projectile Motion is an essential physics tool for determining how long a projectile remains in the air after being launched. Time of flight is the total duration from launch until the projectile hits the ground. This calculator uses the kinematic equations of projectile motion to compute the flight time, accounting for initial velocity, launch angle, initial height, and gravitational acceleration. Understanding time of flight is crucial for analyzing trajectories, predicting landing points, and solving projectile motion problems in physics and engineering.
When to Use This Calculator
- Physics Homework: Solve problems involving time of flight calculations for projectiles
- Sports Analysis: Calculate how long a ball stays in the air during sports like basketball, football, or baseball
- Engineering Design: Determine flight times for projectiles in mechanical systems or safety assessments
- Ballistics: Analyze flight duration for bullets, arrows, or other projectiles
- Safety Planning: Calculate flight times for fireworks, rockets, or other launched objects
- Educational Purposes: Understand the relationship between launch parameters and flight duration
Why Use Our Calculator?
- ✅ Accurate Calculations: Uses precise kinematic equations for projectile motion
- ✅ Handles Initial Height: Accounts for projectiles launched from elevated positions
- ✅ Multiple Outputs: Provides time of flight, time to max height, and range
- ✅ Customizable Gravity: Adjust gravitational acceleration for different planets or scenarios
- ✅ Educational Value: Shows formulas and step-by-step calculations for learning
- ✅ Instant Results: Get time calculations immediately without manual computation
Common Applications
Sports Physics: Calculate how long a basketball shot, football kick, or baseball hit stays in the air, helping athletes understand trajectory timing and optimize their technique.
Engineering Projects: Determine flight times for projectiles in mechanical launching systems, automated throwing devices, or safety barrier assessments.
Physics Education: Help students understand how launch angle, initial velocity, and initial height affect flight time, demonstrating key concepts in kinematics.
Safety Planning: Calculate flight times for fireworks, rockets, or other projectiles to ensure proper timing and safe launch distances.
Tips for Best Results
- Use Consistent Units: Ensure all inputs use meters (m) for distance and meters per second (m/s) for velocity
- Check Angle Range: Launch angles should be between 0° (horizontal) and 90° (vertical) for meaningful results
- Consider Air Resistance: This calculator assumes no air resistance; real-world flight times will differ
- Initial Height Matters: Don't forget to include initial height if the projectile starts elevated; it significantly affects flight time
- Symmetric Trajectories: For ground-level launches, time to max height is exactly half the total flight time
Frequently Asked Questions
What is time of flight?
Time of flight is the total duration a projectile spends in the air from launch until it hits the ground. It's calculated using kinematic equations that account for the projectile's initial velocity, launch angle, initial height, and gravitational acceleration.
How does launch angle affect time of flight?
For projectiles launched from ground level, time of flight increases as the launch angle approaches 90° (vertical). At 90°, flight time is maximum (2v₀/g). At 45°, flight time is also significant and corresponds to maximum range. At 0° (horizontal), flight time is minimal (just the time to fall from initial height).
What is the relationship between time of flight and time to max height?
For symmetric trajectories (launched from ground level, h₀ = 0), the time to reach maximum height is exactly half the total time of flight. This is because the upward and downward portions of the trajectory are symmetric. The formula is: t_max = T/2 = v₀ sin(θ) / g.
How does initial height affect flight time?
Initial height increases time of flight because the projectile has more time to fall. The formula accounts for this with the term √(v₀² sin²(θ) + 2gh₀) in the numerator. Higher initial height means the projectile spends more time in the air before hitting the ground.
Does this calculator account for air resistance?
No, this calculator assumes no air resistance, which is valid for low speeds and dense objects. For high-speed projectiles or light objects, air resistance reduces flight time because drag slows the projectile down more than gravity alone would.
Can I use this for projectiles on other planets?
Yes! Simply change the gravity value. For example, use g = 1.62 m/s² for the Moon (longer flight times), g = 3.71 m/s² for Mars, or g = 24.79 m/s² for Jupiter (shorter flight times). Lower gravity means longer flight times.