PROJECTILE MOTION CALCULATOR

Projectile motion calculator calculates the initial velocity (V0), initial angle (α), flight duration (t), horizontal distance (or range) (l) and maximum height (h) of a projectile motion in physics. The effect of air resistance is ignored.

Projectile Motion Calculator

Formulas used in the projectile motion calculator are given below.

Projectile Motion Formulas

If the initial velocity (V0) and angle (α) parameters are known;

$$l=\frac { { { V }_{ 0 } }^{ 2 }\sin { 2\alpha } }{ g }$$
$$h=\frac { { { { (V }_{ 0 } }\sin { \alpha } ) }^{ 2 } }{ 2g }$$
$$t=\frac { 2V\sin { \alpha } }{ g }$$

If the initial velocity(V0) and flight duration (t) parameters are known;

$$l=\sqrt { { { V }_{ 0 } }^{ 2 }-{ (\frac { gt }{ 2 } ) }^{ 2 } } t$$
$$h=\frac { g{ t }^{ 2 } }{ 8 }$$
$$\alpha =\tan ^{ -1 }{ \frac { 4h }{ l } }$$

If the initial velocity(V0) and maximum height (h) parameters are known;

$$\alpha =\arcsin { \frac { \sqrt { 2gh } }{ { V }_{ 0 } } }$$
$$l=\frac { { { V }_{ 0 } }^{ 2 }\sin { 2\alpha } }{ g }$$
$$t=\frac { 2V\sin { \alpha } }{ g }$$

If the maximum height (h) and travel distance (l) parameters are known;

$${ V }_{ 0 }=\frac { \sqrt { 2gh } }{ \sin { \alpha } }$$
$$\alpha =\tan ^{ -1 }{ \frac { 4h }{ l } }$$
$$t=2\sqrt { \frac { 2h }{ g } }$$

If the flight duration (t) and travel distance (l) parameters are known;

$${ V }_{ 0 }=\sqrt { { (\frac { l }{ t } ) }^{ 2 }+{ (\frac { gt }{ 2 } ) }^{ 2 } }$$
$$\alpha =\tan ^{ -1 }{ \frac { g{ t }^{ 2 } }{ 2l } }$$
$$h=\frac { g{ t }^{ 2 } }{ 8 }$$