What is the difference between equation and formula?

Sometimes equation and formula are used interchangeably, but I was wondering if there is a difference.

For example, suppose we can calculate a car's fuel efficiency as:

mpg = distance traveled in miles / the fuel used in a gallon

Is that an equation or formula?

Solution 1:

An equation is any expression with an equals sign, so your example is by definition an equation. Equations appear frequently in mathematics because mathematicians love to use equal signs.

A formula is a set of instructions for creating a desired result. Non-mathematical examples include such things as chemical formulas (two H and one O make H2O), or the formula for Coca-Cola (which is just a list of ingredients). You can argue that these examples are not equations, in the sense that hydrogen and oxygen are not "equal" to water, yet you can use them to make water.

Mathematicians have long since realized that when it comes to numbers, certain formulas can be expressed most succinctly as equations. For example, the Pythagorean Theorem $a^2+b^2=c^2$ can be thought of as a formula for finding the length of the side of a right triangle, but it turns out that such a length is always equal to a combination of the other two lengths, so we can express the formula as an equation. The key idea is that the equation captures not just the ingredients of the formula, but also the relationship between the different ingredients.

In your case, "mpg = distance/gallons" is best understood as "a formula in the form of an equation", which means that in this instance the two words are interchangeable.

Solution 2:

An equation is meant to be solved, that is, there are some unknowns. A formula is meant to be evaluated, that is, you replace all variables in it with values and get the value of the formula.

Your example is a formula for mpg. But it can become an equation if mpg and one of the other value is given and the remaining value is sought.

Solution 3:

I'd say an equation is anything with an equals sign in it; a formula is an equation of the form $A={\rm\ stuff}$ where $A$ does not appear among the stuff on the right side.

Solution 4:

Please down vote me if you wish - but I would say these words are really synonyms to each other. They both express that there is some underlying relation between some mathematical expressions.

Solution 5:

A formula is an equation that shows the relationship between two or more quantities. It would be the rule or instructions that is use to show the relationship between two or more quantities.

An equation is a problem displayed with numerals or symbols with an equals (=) sign included somewhere; usually near the end of the equation. Unless, it is a ratio or division.