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Physics Help >> Index to Physics Homework Help » Converting Units

Using Conversion Factors


Converting units is like riding a bicycle: once you know how it’s easy. One method is to multiply the given unit by a conversion factor that cancels the unwanted unit and replaces it with the desired unit.

For example, to convert 2 hours to minutes you intuitively multiply by 60. But why does that work?


Using dimensional analysis, multiplying hours by minutes per hour converts hours to minutes because hours cancel.


You see that h is in both the numerator and the denominator, so the h cancels, leaving you with minutes. (Related term: dimensional analysis.)


A common problem is how to convert grams to kilograms. For example, how many kg is 250 g?


250 g x (1 kg)/(1000 g) = 0.25 kg


Converting km/h to m/s


If you have two units at a time, you use two conversion factors. For example, to convert 50 km/h to m/s you convert km to m and 1/ h to 1/ s:


To convert km per h to m per s, multiply be m per km and by h per s.

Converting three units at a time, requires you use three conversion factors. For example, to convert 50 mi/h to m/s you convert mi to km, km to m and 1/ h to 1/ s:


To convert mi/h to m/s requires converting mi to km, km to m, and h to s.



Converting mph to m/s


To convert miles per hour to m/s, we recall that there are 1.61 km in a mile, 1000 m in a km, and 3600 seconds in an hour:


60.6 mph * (1.61 km/mi)(1000m/km)(1h/3600s) = 60.6 * (.447) =27.1 m/s


Metric Conversions


Another method works well for converting between metric units. For example, the axon of a neuron has a diameter of 0.20 microns. Express this diameter in terms of nanometers.

(1 micron = 1 micrometer).


Metric conversions may be done easily be replacing the prefix with power of 10, multiplying by one, then replacing the power of 10 with a prefix.


(Related search term: metric multipliers, SI multipliers, metric prefix.)



Metric conversion is a free online service for converting units of length, weight, speed, temperature, time, volume, area, power and energy

a. A building is 555 ft high. Express this height in meters.
b. A man is 7 ft tall. What is his height in meters?

2. A filament has a diameter of 0.20 microns. Express this diameter in terms of a centimeter. (1 micron = 1 micrometer).

3. Change the following to the SI unit and in standard form:

a. 2.31 MJ

b. 1.5 gcm-3

4. Convert 10 km/hr/s to m/s2.





For solutions to all the problems on this page click here.





(10 km/h/s)*(1000 m / km)*(3600 s / h) = 2.78 m/s/s = 2.78 m/s2