## Time Dilation Calculator :

Enter the time dilation calculator, calculates the Time interval (Δt) in seconds(sec), Observer velocity (v) in km/s, Relative time (Δt’) in seconds(sec), and you get the calculator check it.

## Time Dilation Formula :

Time Dilation Formula is time observed T_{(s)} in second is equal to the time observed at rest T_{0(s)} in second and divided by the root of one minutes square of the velocity of the object v^{2}_{(m/kg)} in meter per kilogram and divided by the velocity of light in vacuum c^{2}_{(m/s2)} in meter per second^{2}.Hence the time Dilation Formula can be written as,

**T _{(s)}=T_{0(s)}/ √1-v^{2}_{(m/kg)}/c^{2}_{(m/s2)}**

where,

T → time observed in second

T_{0} → time observed at rest in second

V→ velocity of the object in m/kg

C → velocity of light in a vacuum (3*10^{8} m/s^{2})

## Sample Problems :

### Example 1 :

Calculate the relativistic time? In a T0 is 4 years and the velocity of the object is 0.30c.

### Solution :

Given,

T_{0}=4years

V=0.30C

The formula for time dilation is given by

T=T/ √1-v^{2}/c^{2}

T=4/√1-(0.30)^{2}(3^{2}*10^{16})/ 3^{2}*10^{16}

T=4/√0.91

T=4/0.9539

T=4.19 years

### Example 2 :

Calculate the relativistic time? In a T0 is 7 years and the velocity of the object is 0.55c.

### Solution :

Given,

T_{0}=7years

V=0.55C

The formula for time dilation is given by

T=T/ √1-v^{2}/c^{2}

T=7/√1-(0.55)^{2}(3^{2}*10^{16})/ 3^{2}*10^{16}

T=7/√0.55^{2}

T=7/0.8351

T=8.38 years