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.
Where Rearrange Equations Is Used
Algebra homework
Checking rearranged formulas step by step.
Physics and science
Solving formulas for speed, force, current or energy.
Geometry
Finding a radius from an area or a side from a perimeter.
Finance basics
Solving the simple interest formula for any variable.
Common Rearrange Equations Mistakes to Avoid
- Work backwards through the order of operations.
- Keep the equals sign balanced at every step.
- Check the answer by substituting back.
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?
Apply the same inverse operations to both sides, undoing the operations around the target variable in reverse order.
What does making a variable the subject mean?
Rewriting the formula so that the variable stands alone on one side.
Why do I take a square root when rearranging a squared term?
The square root undoes the square, so r² = A/π becomes r = √(A/π).
Can I rearrange any formula with this tool?
It covers the common formulas in the list, each with all its rearrangements.