Convert MPG to Liters per 100km

While residents in the United States are used to seeing fuel efficiency as mpg (miles per gallon), there are many other areas of the world that use l/100 km (liters per 100 kilometers). To convert you can use a simple formula and complete the necessary calculation. If you are converting from imperial gallons, you can use the formula <math>L/100 \text{km} = \frac{282.48}{x \; \text{mpg}}</math>. If you are converting from US gallons, you can use the formula <math>L/100 \text{km} = \frac{235.21}{x \; \text{mpg}}</math>. Another option is to set up a series of ratios that will lead you from one unit to the desired units.

Steps

Using the Conversion Formula

  1. Determine which type of gallon you are converting from. Gallons can be imperial or US Imperial gallons are used in the UK, and US gallons are used in the US. Since these two types of gallons are not the same, the conversion formula will be different depending on which type of gallon you are converting from.
    • If the problem does not specify which type of gallon, and you are a student in the United States, it is probably safe to assume that you are converting from US gallons.
    • Outside of the United States, it is probably safe to assume that you are converting from the imperial gallon.
  2. Set up the formula for converting from miles per imperial gallons. The formula is <math>L/100 \text{km} = \frac{282.48}{x \; \text{mpg}}</math>.[1] Substitute the number of miles per gallon into the formula, then divide. The quotient will give you the equivalent number of liters per 100 km.
    • For example, if you are converting 24 miles per imperial gallon to liters per 100 km, you would calculate:
      <math>L/100 \text{km} = \frac{282.48}{24}</math>
      <math>L/100 \text{km} = 11.77</math>
      So, 24 MPG (imperial) is equal to 11.77 L/100km.
  3. Set up the formula for converting from miles per US gallon. The formula is <math>L/100 \text{km} = \frac{235.21}{x \; \text{mpg}}</math>.[2] Plug the number of miles per gallon into the formula. Divide the MPG into 235.21. The result will be the converted number of liters per 100 km.
    • For example, if you are converting 24 miles per US gallon to liters per 100 km, you would calculate:
      <math>L/100 \text{km} = \frac{235.21}{24}</math>
      <math>L/100 \text{km} = 9.8</math>
      So, 24 MPG (US) is equal to 9.8 L/100km.

Setting up Ratios

  1. Determine whether you are working with imperial or US gallons. These two types of gallons are not the same size, and thus the numbers you use in your ratios will be different depending on which type you are working with.
    • 1 imperial gallon is equal to 4.55 liters.[3]
    • 1 U.S. gallon is equal to 3.79 liters.[3]
  2. Set up a ratio for converting miles per gallon to kilometers per gallon. There are 1.609 kilometers in a mile, so your ratio will look like this:<math>\frac{x \; \text{mi}}{1 \text{gallon}} \times \frac{1.609 \text{km}}{1 \text{mi}}</math>. Multiply the number of miles times 1.609 to find out how many kilometers per gallon.[4]
    • For example, to convert 24 MPG, you would calculate:
      <math>\frac{24 \text{mi}}{1 \text{gallon}} \times \frac{1.609 \text{km}}{1 \text{mi}} = \frac{38.616 \text{km}}{1 \text{gallon}}</math>
  3. Set up a ratio converting kilometers per gallon to kilometers per liter. Your ratio will look different, depending on whether you are working with imperial or US gallons. Since we want to find liters per 100 km, you need to take the reciprocal of your final ratio so that the liters value is in the numerator.[4]
    • If you are working with imperial gallons, you will calculate: <math>\frac{38.616 \text{km}}{1 \text{gallon}} \times \frac{1 \text{gallon}}{4.55 \text{liters}} = \frac{38.616 \text{km}}{4.55 \text{liters}}</math>. Taking the reciprocal, you have <math>\frac{4.55 \text{liters}}{38.616 \text{km}}</math>.
    • If you are working with US gallons, you will calculate: <math>\frac{38.616 \text{km}}{1 \text{gallon}} \times \frac{1 \text{gallon}}{3.79 \text{liters}} = \frac{38.616 \text{km}}{3.79 \text{liters}}</math>.Taking the reciprocal, you have <math>\frac{3.79 \text{liters}}{38.616 \text{km}}</math>.
  4. Calculate the rate of liters per 1 kilometer. To do this you need to get the number of kilometers in the ratio to 1 by dividing. Divide the numerator and the denominator of the ratio by the number of kilometers. You can also think of it as dividing the numerator by the denominator.
    • For example, for imperial gallons, you would calculate <math>\frac{4.55 \text{liters}}{38.616 \text{km}} = .118 \; \text{liters per km}</math>.
    • For US gallons, you would calculate <math>\frac{3.79 \text{liters}}{38.616 \text{km}} = .098 \; \text{liters per km}</math>.
  5. Calculate the rate of liters per 100 kilometers. To do this, multiply the rate of liters per km by 100.[4] You can do this easily in your head by moving the decimal point two places to the right.
    • For example, if the rate in imperial gallons is <math>.118 \; \text{liters per km}</math>, to calculate liters per 100 km, multiply <math>.188 \times 100 = 18.8 \; \text{liters per 100 km}</math>.
    • If the rate in US gallons is <math>.098 \; \text{liters per km}</math>, to calculate liters per 100 km, multiply <math>.098 \times 100 = 9.8 \; \text{liters per 100 km}</math>.

Converting L/100 km to MPG

  1. Convert to miles per imperial gallon using a conversion formula. The formula is <math>\text{mpg} = \frac{282.48}{x \; L/100 \text{km}}</math>.[1] To find the miles per gallon, divide the number of liters per 100 km into 282.48.
    • For example, if calculating 20 L/100 km to mpg, you would calculate:
      <math>\text{mpg} = \frac{282.48}{20}</math>
      <math>\text{mpg} = 14.124</math>.
  2. Convert to miles per US gallon using a conversion formula. The formula is <math>\text{mpg} = \frac{235.21}{x \; L/100 \text{km}}</math>.[2] To find the miles per gallon, divide the number of liters per 100 km into 235.21.
    • For example, if calculating 20 L/100 km to mpg, you would calculate:
      <math>\text{mpg} = \frac{235.21}{20}</math>
      <math>\text{mpg} = 11.76</math>.
  3. Convert to miles per imperial gallon using a ratio. Set up the ratio <math>\text{mpg} = \frac{x \; \text{liters}}{100 \text{km}}</math>. Then complete the necessary calculations to convert to miles per imperial gallon.
    • First, convert the number of liters per 100 km to the number of liters per 1 km. If you were converting 20 liters per 100 km, you would first calculate <math>\frac{20 \text{liters}}{100 \text{km}} = \frac{.20 \text{liters}}{1 \text{km}}</math>.
    • Second, convert liters per kilometer to liters per miles. There are .62 miles in one kilometer.[5] So, to convert, you would calculate <math>\frac{.20 \text{liters}}{1 \text{km}} \times \frac{1 \text{km}}{.62 \text{mi}} = \frac{.20 \text{liters}}{.62 \text{mi}}</math>.
    • Third, convert the number of liters to the number of imperial gallons. There are .22 imperial gallons in a liter.[3] To convert, you would calculate <math> \frac{.20 \text{liters}}{.62 \text{mi}} \times \frac{.22 \text{gallons}}{.1 \text{liters}} = \frac{.044 \text{gallons}}{.62 \text{mi}}</math>.
    • Fourth, since you want to find miles per gallon, take the reciprocal of the fraction:<math>\frac{.62 \text{mi}}{.044 \text{gallons}}</math>.
    • Last, find the number of miles per gallon by dividing the numerator and the denominator by the number of gallons:<math>\frac{.62 \text{mi}}{.044 \text{gallons}} = 14.1 \; \text{mpg}</math>.
  4. Convert to miles per US gallon using a ratio. Set up the ratio <math>\frac{x \; \text{liters}}{100 \text{km}}</math>. Then complete the necessary calculations to convert to miles per imperial gallon.
    • First convert the number of liters per 100 km to the number of liters per 1 km. If you were converting 20 liters per 100 km, you would first calculate <math>\frac{20 \text{liters}}{100 \text{km}} = \frac{.20 \text{liters}}{1 \text{km}}</math>.
    • Second, convert liters per kilometer to liters per miles. There are .62 miles in one kilometer.[5] So, to convert, you would calculate <math>\frac{.20 \text{liters}}{1 \text{km}} \times \frac{1 \text{km}}{.62 \text{mi}} = \frac{.20 \text{liters}}{.62 \text{mi}}</math>.
    • Third, convert the number of liters to the number of US gallons. There are .26 US gallons in a liter.[3] To convert, you would calculate <math> \frac{.20 \text{liters}}{.62 \text{mi}} \times \frac{.26 \text{gallons}}{.1 \text{liters}} = \frac{.052 \text{gallons}}{.62 \text{mi}}</math>.
    • Fourth, since you want to find miles per gallon, take the reciprocal of the fraction:<math>\frac{.62 \text{mi}}{.052 \text{gallons}}</math>.
    • Last, find the number of miles per gallon by dividing the numerator and the denominator by the number of gallons:<math>\frac{.62 \text{mi}}{.052 \text{gallons}} = 11.92 \; \text{mpg}</math>.



Related Articles

  • Convert-Liters/100-Kilometer-to-Mpg

Sources and Citations

  1. ↑ 1.0 1.1 http://www.aqua-calc.com/convert/fuel-consumption/liter-per-100-kilometer-to-mile-per-imperial-gallon
  2. ↑ 2.0 2.1 https://www.nrcan.gc.ca/energy/efficiency/transportation/7471
  3. ↑ 3.0 3.1 3.2 3.3 http://www.gallonstoliters.com/
  4. ↑ 4.0 4.1 4.2 https://www.illustrativemathematics.org/content-standards/tasks/930
  5. ↑ 5.0 5.1 http://www.metric-conversions.org/length/kilometers-to-miles.htm
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