Train questions test relative speed and unit conversion. Enter both lengths and speeds and choose whether the other object is still, moving the same way or coming towards the train.
Enter the train's length and speed.
Enter the other object's length and speed.
Choose its direction and read the time.
Time: t = (L₁ + L₂) ÷ relative speed
Unit change: km/h × 5/18 = m/s
Train problems ask how long a train takes to pass a pole, a platform, a bridge or another train. The answer depends on two ideas: the distance covered is the sum of the lengths involved, and the speed is the relative speed between the train and the object. This calculator applies both, including the km/h to m/s conversion that trips up many students.
The topic is a favourite in SSC, RRB NTPC, banking and state recruitment exams because it tests unit sense and relative motion in one question. It also helps with everyday curiosity, such as how long a Rajdhani takes to clear a station platform.
Enter the train's length and speed, the other object's length and speed, and whether it is stationary, moving the same way or coming the opposite way.
1. Find the relative speed: the train's speed if the object is still, the difference of speeds if both move in the same direction, the sum if they move towards each other.
2. Convert km/h to m/s by multiplying by 5/18.
3. Find the distance to cover: train length + length of the object. A pole, signal or person has length 0.
4. Compute time = distance ÷ relative speed, in seconds.
5. To convert back, multiply m/s by 18/5 to get km/h.
6. For reverse questions, rearrange: length = speed × time − other length.
Crossing starts when the front of the train reaches the start of the object and ends when the rear of the train leaves its far end. In that time the front of the train travels its own length plus the length of the object. For a pole, which has no length, the front travels only the train's own length. For two trains, the same logic uses the relative motion: the gap closed is the sum of both train lengths.
Relative speed is the speed of one object as seen from the other. If both move the same way at 72 and 54 km/h, the faster gains on the slower at 18 km/h. If they approach each other, each closes the gap, so the relative speed is 126 km/h. Measured from the second train, the first is simply a train moving at the relative speed past a stationary object, which reduces the problem to the simple case. If relative speed is zero, the trains never cross.
One kilometre is 1,000 metres and one hour is 3,600 seconds, so 1 km/h = 1,000 ÷ 3,600 m/s = 5/18 m/s. Train lengths are given in metres, so speeds must be in m/s to give time in seconds. Common values worth remembering: 36 km/h = 10 m/s, 54 km/h = 15 m/s, 72 km/h = 20 m/s and 90 km/h = 25 m/s. Spotting these saves time in exams.
A 180 m long express train running at 54 km/h meets a 120 m long goods train coming from the opposite direction at 36 km/h on the parallel track.
Relative speed: 54 + 36 = 90 km/h
Convert to m/s (× 5/18): 90 × 5 ÷ 18 = 25 m/s
Distance to cover = both lengths: 180 + 120 = 300 m
Time = distance ÷ speed: 300 ÷ 25 = 12 s
Answer: Time to cross 12 seconds; Relative speed 25 m/s (90 km/h); Distance covered 300 m
Forgetting to convert km/h to m/s before dividing metres by speed.
Using only the train's length when crossing a platform or bridge.
Adding speeds for trains moving in the same direction.
Multiplying by 18/5 instead of 5/18 when converting to m/s.
Treating a man walking on the platform as stationary when the question gives his speed.
Solving RRB, SSC and banking aptitude questions.
Estimating how long a train takes to clear a level crossing or platform.
Teaching relative motion in physics and maths classes.
Checking train length from crossing time and speed.
Why is a pole's length zero?
A pole or a person is treated as a point, so the train only covers its own length.
Why add speeds for opposite directions?
Each train closes the gap, so they approach each other at the sum of their speeds.