Substituting into Equations and Formula

A major part of this course is algebra-based, namely, learning how manipulate equations, combine like-term, and evaluate expressions. This lesson will give you a sense of what’s to come in future lessons.

formula is an equation expressing some general mathematical or physical fact, such as the formula for the area of a circle of radius r:


Notice how the formula has 2 unknowns, A and r – π isn’t an unknown, it represents approximately 3.14159… To find the area of any circle, you substitute any value in for r. For example, if r = 4 cm:


On the contrary, you could substitute a value in for A, then solve for r via algebraic manipulation, which we’ll cover later on in the course. Regardless of what you’re looking for, it’s always appropriate to enclose the number you substitute in parentheses (round brackets), as shown in the example above.

Therefore, to substitute into a formula or equation means to replace the letter quantities in the formula with their numerical values, and evaluate. Let’s do a few examples where we substitute values into formulas: