Free Fall Formulas

Free fall formulas, which are used for free fall height, final velocity and fall time calculations, are given in the following charts. The effect of air resistance is ignored in the formulas.

Parameter Formula
Free Fall Height [h] \(h=x{ -x }_{ 0 }={ v }_{ 0 }t+1/2g{ t }^{ 2 }\)
\(h=x{ -x }_{ 0 }=\frac { (v+{ v }_{ 0 })t }{ 2 } \)
Final Velocity [v] \(v={ v }_{ 0 }+gt\)
\(v=\sqrt { { v }_{ 0 }^{ 2 }+2g(x-{ x }_{ 0 }) }\)
Fall Time [t] \(t=(v-{ v }_{ 0 })/g\)
\(t=\frac { -{ v }_{ 0 }\pm \sqrt { { v }_{ 0 }^{ 2 }+2gh } }{ g } \)

 

If the initial velocity (v0) and position (x0) are 0 (free falling object is at rest), then the following formulas are used.

Parameter Formula
 Free Fall Height [h] \(h=\frac { 1 }{ 2 } g{ t }^{ 2 }\)
\(h={ v }^{ 2 }/g\)
 Final Velocity [v] \(v=\sqrt { \ { 2gh } }\)
 \(v=gt\)
Fall Time [t] \(t=\sqrt { \frac { 2h }{ g } }\)
 \(t=v/g\)

 

The list of parameters and their definitions are given below.

Parameter Definition
x0 Initial Position
x Final Position
v0 Initial Velocity
v Final Velocity
h Free Fall Height
t Fall Time
g Gravity

 

Additional Resources