Formulas and Equations

Formulas and equations are used in many areas of science. Both formulas and equations show the relationships between quantities. Any numerical sentence that contains at least one variable and at least one mathematical operator is called an equation. A formula is a type of equation that states the relationship between unknown quantities represented by variables.

For example, Speed = Distance ÷ Time is a formula, because no matter what values are inserted, speed is always equal to distance divided by time. The relationship between the variables does not change.

Example

Follow these steps to convert a temperature measurement of 50°F to Celsius.

1. Determine the formula that shows the relationship between these quantities.

   °F = (9/5 X °C) + 32°F

2. Insert values you know into the formula.

   50°F = (9/5 X °C) + 32°F

3. Solve the resulting equation.

   50°F − 32°F = (9/5 X °C)

   18°F = 9/5 X °C

   18°F × 5/9 = 10°C

Applying Formulas and Equations

There are many applications of formulas in science. The example described below uses a formula to calculate density.

Example

Follow these steps to calculate the density of an object that has a mass of 45 g and a volume of 30 cm³.

1. Determine the formula that shows the relationship between these quantities.

   Density = Mass/Volume

2. Insert values you know into the formula.

   Density = 45 g/30 cm³

3. Solve the resulting equation.

   Density = 1.5 g/cm³