Literal Equation Solver Calculator

Enter Calculation

Choose a literal equation to solve Triangle area: A = ½·b·h → solve for h Rectangle area: A = L·W → solve for W Distance: d = r·t → solve for r Ohm law: V = I·R → solve for R Simple interest: I = P·r·t → solve for r Linear: y = m·x + b → solve for x

First known value

Second known value

Third known value (if needed)

Enter the known quantities in equation order. Example for A=½bh → solve h: First = A, Second = b.

Results

Solved value of h

h = 8

isolated target variable

Step	h = 2A / b = (2 × 20.0) / 5.0
Result	h = 8

What is a literal equation?

A literal equation is a formula that contains several letters (variables) rather than only numbers. Examples include the area of a triangle \(A = \tfrac{1}{2}bh\), distance \(d = rt\), Ohm law \(V = IR\), and the slope-intercept line \(y = mx + b\). Solving a literal equation means rearranging it so that one chosen variable stands alone on one side of the equals sign. This calculator does that rearrangement and then plugs in your known values to return the missing variable.

How to use this calculator

Pick the equation you are working with from the dropdown. Each option already states which variable will be solved. Then enter the known quantities in the order shown in the label (First, Second, and a Third when the formula needs three knowns). The calculator applies inverse operations — undoing multiplication with division, and undoing addition with subtraction — and reports the isolated variable plus the step it used.

The method explained

To isolate a variable you reverse every operation attached to it, in the opposite order. For \(A = \tfrac{1}{2}bh\), the height \(h\) is multiplied by ½ and by \(b\), so you divide both sides by ½b, giving \(h = \frac{2A}{b}\). For \(y = mx + b\) you first subtract \(b\) from both sides, then divide by \(m\), giving \(x = \frac{y - b}{m}\). The same logic generalizes to every formula in the menu.

Isolating a variable: apply the same inverse operation to both sides to keep the equation balanced.

Worked example

Suppose a triangle has area A = 20 and base b = 5, and you want the height. Using \(h = \frac{2A}{b}\):

$$h = \frac{2 \times 20}{5} = \frac{40}{5} = \mathbf{8}$$

So the height is 8 units.

Step-by-step rearrangement of \(A = \tfrac{1}{2}bh\) to solve for \(h\).

FAQ

Which value goes in each box? The label tells you: First is the first letter in the equation (often the result, like A or d), Second is the next, and Third is used only for three-term formulas such as simple interest.

Why did I get 0? A divisor turned out to be zero (for example b = 0). Division by zero is undefined, so the calculator returns 0 as a guard.

Can it handle negatives and decimals? Yes — enter any real number, including negatives and decimals, and the inverse operations still apply.