How to Calculate the Jump Height From Acceleration

With physics, you can calculate how high you jump.
••• Ezra Shaw/Digital Vision/Getty Images

Problems dealing with motion are usually the first that students of physics will encounter. Concepts like time, velocity and acceleration are interrelated by formulas that students can rearrange with the help of algebra to apply to different circumstances.

Students can calculate the height of a jump, for instance, from more than one starting point. The height of the jump can be calculated if the acceleration and either the initial velocity or the total time in the air is known.

Write an expression for time in terms of change in velocity, using the formula


where ​vf is final velocity, ​g​ is the acceleration due to gravity, ​t​ is time, and ​vi is initial velocity.

Time of Flight

Solve the equation for ​t

t = (v_f − v_i)/-g

Therefore, the amount of time is equal to the change in velocity divided by the acceleration due to gravity.

Calculate Time to Reach Highest Point

Calculate the amount of time to reach the highest point of the jump. At the highest point, velocity (​vf) is zero. Use 9.8 m/s² for the acceleration due to gravity. For example, if the initial velocity is 1.37 m/s, time to reach maximum height is:

t = (0 − 1.37)/( − 9.8) = 0.14\text{ s}

Calculate Initial Velocity from Total Time of Flight

The initial velocity ​vi can be calculated using the time to reach the jump height


For example, if the total time is 0.14 seconds:

v_i=9.8\times 0.14=1.37\text{ m/s}

Vertical Jump Physics Equation

Calculate the jump height using the formula


where ​sf is the final position and ​si is the initial position. Since jump height is the difference between the final and initial position

h = (s_f − s_i)

simplify the formula to


and calculate:

h = (1.37\times 0.14) - 1/2(9.8 \times 0.14^2) = 0.19 − 0.10 = 0.09\text{ meters}


  • Create your own jump height calculator by programming the jump height formula into your graphing calculator!

Related Articles

How to Calculate the Velocity of an Object Dropped...
How to Solve a Time in Flight for a Projectile Problem
How to Calculate How Long it Takes an Object to Fall
How to Convert Seconds Into Miles Per Hour
How to Find Mass in Weight
How to Find the Height of a Rectangular Pyramid
How to Find a Distance From Velocity & Time
How to Calculate a Change in Momentum
How to Find the Area of Squares
How to Calculate Tangential Speed
How to Calculate the Diameter of a Circle From a Linear...
How to Calculate Height & Velocity
How to Calculate the Temperature Drop Due to a Pressure...
How to Calculate Velocity of Falling Object
How to Calculate Percent Relative Range
Test Your Knowledge on Middle School Science
How to Calculate Area of a Triangle
How to Convert Pounds Per Square Foot to PSI
How to Calculate Perimeter and Area Ratio
How to Calculate Cost Increase by a Percent

Dont Go!

We Have More Great Sciencing Articles!