Projectile Maximum Height

H = \frac{v_0^2 \sin^2(\theta)}{2g}

Maximum height of a projectile.

Variables

Maximum height

Peak height reached

v₀

Initial velocity

Launch speed

m/s

Launch angle

Angle above horizontal

In SI units: rad

Gravitational acceleration

≈ 9.8 m/s²

Allowed values: greater than 0

m/s²

Derivation

At max height, v_y = 0. Use v² = v₀² - 2gh.

Your notes

0/5000

Constants in this formula

Standard Gravity

9.806 65. Exact by definition.

m/s²

Check value

Round inputs run through this page's calculator, with each constant at its tabulated value. Use it to test your own working or a rearranged form. It is a test case, not a real-world example.

v₀ = 2 m/s (Initial velocity)
θ = 3 ° (Launch angle)
g = 9.806 65 m/s² (Gravitational acceleration)

Result: H = 0.00055861 m

Other mechanics formulas with the same quantities

Projectile Time of Flight (Kinematics) shares Initial velocity, Launch angle, Gravitational acceleration
Kinematic Equation 1 (Kinematics) shares Initial velocity
Kinematic Equation 2 (Kinematics) shares Initial velocity
Kinematic Equation 3 (Kinematics) shares Initial velocity
Kinematic Equation 4 (Kinematics) shares Initial velocity
Weight (Dynamics) shares Gravitational acceleration

Where this formula is listed

Mechanics formulas, under Kinematics, alongside Velocity, Acceleration and Average Velocity.
In the mechanics list it comes after Projectile Range and before Projectile Time of Flight.
Mechanics formula sheet, one of 58 formulas printed with symbol keys and SI units.
The full formula index, grouped by category and topic.

Common questions

What is the Projectile Maximum Height formula?

Projectile Maximum Height is written H = (v₀² sin²(θ))/(2g). Maximum height of a projectile. It belongs to Mechanics, under Kinematics.

What are the units in H = (v₀² sin²(θ))/(2g)?

In SI units, H is maximum height, measured in m; v₀ is initial velocity, measured in m/s; θ is launch angle, measured in rad; g is gravitational acceleration, measured in m/s².

How is the Projectile Maximum Height formula derived?

At max height, v_y = 0. Use v² = v₀² - 2gh. The result is H = (v₀² sin²(θ))/(2g).