What Is Rearrange Equations?
Rearranging an equation, also called changing the subject of a formula, means rewriting it so one chosen variable stands alone on one side. You do it by applying the same inverse operation to both sides, undoing the operations around the variable in reverse order.
Pick a formula, such as a straight line, speed, distance and time, Ohm's law, the area of a circle, simple interest or kinetic energy, type the symbol you want as the subject, and enter the other values. The calculator shows the rearranged equation, each step, and the numerical answer, along with a table of the variables.
The sections below list the formulas, explain the variables, work through an example and answer common questions about rearranging and the order of operations.
How to Use the Rearrange Equations Calculator
- Choose a formula.
- Type the symbol of the variable you want as the subject.
- Enter the other values as symbol=number.
- Read the rearranged formula, the steps and the answer.
Rearrange Equations Formula
Straight line
Circle area
Velocity
Rearrange Equations Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| Subject | The variable to isolate | |
| Known values | Numbers for every other variable | entered as symbol=number |
| Inverse operation | The operation that undoes another | divide undoes multiply |
| √ | Square root | undoes a squared term |
Rearrange Equations Worked Example
Rearrange d = s t to find speed. Divide both sides by t to get s = d ÷ t. For d = 150 and t = 2.5, s = 150 ÷ 2.5 = 60.
With the example values loaded in the calculator above, the steps are:
- Start with d = s t.
- Divide both sides by t: s = d / t.
- Substitute d = 150, t = 2.5.
- s = 60.
Result: s = = 60; Rearranged formula = s = d / t.
How to Read a Rearranged Equation
Making a variable the subject puts it alone on the left, so you can compute it directly. For d = s·t, dividing both sides by t gives s = d ÷ t. With d = 150 and t = 2.5, s = 60.
Each step changes both sides in the same way, so the equation stays true. Always substitute your answer back into the original formula to check it. The table lists the variables in the formula so you know what each symbol means.
Where Rearrange Equations Is Used
Physics formulas
Make speed, distance or time the subject of a formula.
Statistics
Solve a formula such as the margin of error for n.
Exams
Check the steps of a rearrangement.
Substituting values
Enter known values and get a number as well as the formula.
Common Rearrange Equations Mistakes to Avoid
- Do the same operation to both sides.
- Undo operations in reverse order.
- Take both the positive and negative root when you undo a square, unless the quantity is positive by nature.
- Check with numbers in the original formula.
Rearrange Equations Terms and Definitions
- Subject of a formula
- The variable written alone on one side of the equals sign.
- Inverse operation
- The operation that undoes another, such as dividing to undo multiplying.
Rearrange Equations FAQs
How do you rearrange an equation?
Undo the operations around the variable one at a time, doing the same to both sides. For d = s·t, divide both sides by t to get s = d ÷ t.
What does making a variable the subject mean?
It means rewriting the equation so that variable stands alone on one side, as in s = d ÷ t.
Why do I take a square root when rearranging a squared term?
Taking the square root undoes the squaring. Remember that x² = k has two solutions, +√k and −√k, unless the variable cannot be negative.
Can I rearrange any formula with this tool?
It handles the formulas it lists, and gives the rearranged form and a numeric answer from the values you enter. For other formulas, follow the same undo-in-reverse steps by hand.