Math
Change the Subject of a Formula
A formula is an equation that specifies how a number of variables are related to another variable.
Formulas are written so that a single variable, the subject of the formula, is on the left side of the equation. All other variables, coefficients, and constants are on the right side of the equation.
For example, in the formula: v = u + at , ‘v’ is the subject.
Formulas are used to calculate the value of the subject when values of all of the other variables are known.
To find ‘v’ in the example, you must substitute values for ‘u’, ‘a’, and ‘t’ in the equation, then evaluate. The answer will equal ‘v’.
To find unknown values of ‘u’, ‘a’, or ‘t’, you can make any of these other variables the subject, instead of ‘v’.
The following steps can be used to change the subject of this formula: v = u + at
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Make ‘u’ the subject of the formula:
According to the order convention, beginning with ‘u’, you add ‘at’ to get ‘v’.
The inverse operation is then to subtract ‘at’:
Subtract ‘at’ from both sides: v - at = u + at - at
Simplify: v - at = u
Swap sides so the subject is on the left hand side: u = v - at
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Make ‘t’ the subject of the formula:
According to the order convention, beginning with ‘t’, you multiply by ‘a’ first, then add ‘u’ to get ‘v’. The inverse operations are to subtract ‘u’ first, then divide by ‘a’.
Subtract ‘u’ from both sides: v - u = u + at - u
Simplify: v - u = at
Divide both sides by 'a':
Simplify:
Swap sides so the subject is on the left hand side:
