Math Formula Calculator

A formula is a rule that connects quantities: $A = \pi r^2$ says the area of a circle is fixed once you know its radius. Using one has three steps.

1. Write the formula down first, before touching any numbers.
2. Replace each letter with its value in brackets. The brackets are not decoration — they keep negatives and multi-digit numbers intact. Substituting $x = -4$ into $x^2$ has to become $(-4)^2 = 16$; without brackets you get $-16$.
3. Evaluate with PEMDAS: brackets, then exponents, then multiply and divide left to right, then add and subtract.

Two things sink most attempts: letters written next to each other mean multiply — $2\pi r$ is $2 \times \pi \times r$ — and units must be consistent before you substitute, since a formula in metres cannot take centimetres.

When the letter you want is not already alone, rearrange the formula and then substitute. It keeps the algebra clean and lets you reuse the result.

The rule is a balance: whatever you do to one side, do to the other. Undo the operations that surround your target, in reverse PEMDAS order — strip the additions first, then the multiplications, then powers and roots.

Rearranging $C = \frac{5}{9}(F - 32)$ for $F$:

$\frac{9}{5}C = F - 32 \quad \Longrightarrow \quad F = \frac{9}{5}C + 32$

The first move multiplies both sides by $\frac{9}{5}$ (the reciprocal of $\frac{5}{9}$), which also removes the bracket; the second adds $32$ to both sides.

The usual error is doing one operation to only part of a side. If you multiply the left by $\frac{9}{5}$, every term on the right gets multiplied too.

Fractions inside a formula are far easier to remove than to work around. Multiply every term on both sides by the LCD of all denominators, and the fractions disappear in one move.

For $\frac{x}{3} + \frac{1}{4} = \frac{5}{6}$, the LCD of $3$, $4$ and $6$ is $12$:

$12 \cdot \frac{x}{3} + 12 \cdot \frac{1}{4} = 12 \cdot \frac{5}{6} \quad \Longrightarrow \quad 4x + 3 = 10$

From there it is ordinary algebra: $4x = 7$, so $x = \frac{7}{4}$.

Two traps. Every term gets multiplied, including the ones without a fraction — miss one and the equation is no longer balanced. And a fraction bar is an invisible bracket: $\frac{x+1}{3}$ multiplied by $3$ gives $x+1$, not $x+1 \div 3$ or just $x$.