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Formula of Speed Distance and Time

Kinematics formulasClass 9ScalarUpdated 1 Nov 2026

speed=distancetime\text{speed} = \frac{\text{distance}}{\text{time}}
SI unit
m/s
Dimensions
[M⁰ L¹ T⁻¹]
where
  • v speed m/s
  • d distance m
  • t time s

The formula of speed distance and time is one relation written three ways: speed=distancetime\text{speed} = \frac{\text{distance}}{\text{time}}, distance=speed×time\text{distance} = \text{speed} \times \text{time} and time=distancespeed\text{time} = \frac{\text{distance}}{\text{speed}}. Know any two of the quantities and the third follows in a single step.

This page is about choosing the right arrangement quickly and handling the units that go with it. Students meet it in Class 6 to Class 9 and in every aptitude style test, and it keeps turning up inside harder physics problems later on.

Quick facts

  • Speed

    v=dtv = \frac{d}{t}

  • Distance

    d=v×td = v \times t

  • Time

    t=dvt = \frac{d}{v}

  • SI units

    m/s, m and s

  • Road units

    km/h, km and h

  • Conversion

    1 m/s = 3.6 km/h

The triangle for the formula of speed distance and time

Draw a triangle and split it with a horizontal line. Put D (distance) in the top half, and S (speed) and T (time) side by side in the bottom half. Cover the quantity you want with a finger:

  • Cover D and you see S beside T, so distance = speed × time.
  • Cover S and you see D over T, so speed = distance ÷ time.
  • Cover T and you see D over S, so time = distance ÷ speed.

The triangle is a memory aid, not a law. It works because all three versions come from one equation, so a quick check of units always tells you whether you picked the right one.

Formula of distance speed and time: examples

Example 1: a marathon pace

A runner finishes a 42.195 km marathon in 3 h 30 min. Find the average speed in km/h and m/s.

Time = 3.5 h.

v=42.1953.5≈12.1 km/hv = \frac{42.195}{3.5} \approx 12.1\ \text{km/h}

In SI: 12.06÷3.6≈3.35 m/s12.06 \div 3.6 \approx 3.35\ \text{m/s}.

Example 2: a delivery drone

A drone flies at 12 m/s for 2.5 minutes. How far does it go?

t = 2.5 × 60 = 150 s.

d=12×150=1800 m=1.8 kmd = 12 \times 150 = 1800\ \text{m} = 1.8\ \text{km}

Example 3: a ferry crossing

A ferry sails 45 km at a steady 18 km/h. How long does the crossing take?

t=4518=2.5 h=2 h 30 mint = \frac{45}{18} = 2.5\ \text{h} = 2\ \text{h}\ 30\ \text{min}

Units that must agree

Matching unit sets for the formula of speed time and distance
DistanceTimeSpeed comes out in
msm/s
kmhkm/h
cmscm/s
kmminkm/min (convert before reporting)

Mixing a row's distance with another row's time gives a wrong number with a wrong unit. Turn every quantity into one set before you calculate. For time, remember that 0.1 h is 6 minutes, so 2.5 h is 2 h 30 min, not 2 h 50 min.

Where the formula needs care

These relations assume the speed is steady, or that v means the average speed over the whole trip. If a journey has stages at different speeds, find the distance and time of each stage, add them, and then divide. The formula of average speed page works through stage problems, including the equal distance trap.

The relation also uses distance, the path length. If a question cares about direction, it is a velocity problem, and the top of the fraction becomes displacement, as on the velocity formula page.

Quick mistakes to avoid

  • Picking the wrong arrangement. Check units: km ÷ h gives km/h, so dividing distance by time gives speed.
  • Decimal hours. 1 h 45 min is 1.75 h.
  • Averaging speeds directly for stages of equal distance.
  • Forgetting to convert before comparing two speeds in different units.

Each arrangement has its own page with more examples: formula of speed, distance formula physics and formula of time, with the wider chapter on kinematics formulas.

Frequently asked questions

Can you give the formula of speed distance and time in one line?

Speed = distance / time. Rearranged, distance = speed × time and time = distance / speed.

How do you find time from speed and distance?

Divide the distance by the speed: t = d / v. Make sure both use the same length unit, such as km with km/h.

What is the formula of time distance and speed in SI units?

With distance in metres and time in seconds, speed comes out in m/s. The relation is the same in any matching set of units.

How do you convert km/h to m/s?

Multiply by 5/18, which is the same as dividing by 3.6. For example, 126 km/h becomes 35 m/s.

Does this formula work if the speed changes?

Yes, if you use the average speed for the whole trip. For changing speed within a stage, use the equations of motion instead.