Interactive Rearranging Formulae Calculator
Select a formula, choose the variable you want to make the subject, then enter the known values.
What is rearranging a formula?
Rearranging formulae (also called formula transposition) means changing which variable is isolated on one side of an equation. In school and university maths, physics, engineering, and chemistry, you often start with a known formula and need to solve it for a different variable.
For example, if you know v = d / t and you need distance, you rearrange to get d = v × t. Same equation, different subject.
How to use this calculator
Step-by-step
- Choose the equation you want to use (for example, Ohm’s Law or Speed-Distance-Time).
- Pick the variable you want to solve for.
- Enter values for all the remaining variables.
- Click Calculate to get the answer instantly.
The tool also shows the rearranged form of the equation so you can learn the algebra, not just the final number.
Common rearrangement patterns
1) Multiplication and division
If a variable is multiplied, divide both sides. If a variable is divided, multiply both sides. Example: from V = I × R, solve for current by dividing both sides by R:
I = V / R
2) Fractions
Clear the denominator carefully. From ρ = m / V, solve for mass by multiplying both sides by V:
m = ρ × V
3) Constants and coefficients
If a variable is multiplied by a constant, divide by that constant. Example from triangle area:
A = (b × h)/2 becomes b = 2A / h.
Worked mini-examples
Example 1: Find time from speed formula
Given d = 150 km and v = 75 km/h, use t = d / v. So:
t = 150 / 75 = 2 hours.
Example 2: Find resistance from Ohm’s Law
Given V = 12 V and I = 3 A, use R = V / I:
R = 12 / 3 = 4 Ω.
Example 3: Find rate using simple interest
If I = 200, P = 1000, t = 2 years, then:
r = I / (P × t) = 200 / (1000 × 2) = 0.1 (10%).
Tips to avoid mistakes
- Use consistent units (seconds with meters, not hours with meters unless converted).
- Watch for division by zero when a variable is in the denominator.
- Keep brackets in the right places, especially with formulas like I = P × r × t.
- Check reasonableness: if a result is huge or negative when it should not be, recheck your entries.
Why this skill matters
Being able to rearrange equations quickly is one of the most useful algebra skills for STEM subjects. Whether you are solving physics equations, engineering formulas, or financial models, making the correct variable the subject saves time and prevents errors.
Use the calculator for speed, then review the rearranged formula shown to reinforce your understanding. Over time, you’ll need the calculator less and your algebra confidence will grow.