The solver shows an equation display at the top with a blinking yellow caret marking the cursor position. Click anywhere in the display to place the cursor, or use arrow keys, Home, and End for keyboard navigation. Type directly or use the button panel below.
Three quick experiments:
• Type V=I⋅R (Ohm's law) and press Enter — the solver detects three variables (V, I, R) and displays target buttons. Click R to solve, then Solve: the result is R=V/I. • Click the "Slope-Intercept" example template — y=mx+b loads. Pick m as the target and the result is m=(y−b)/x. • Try the "Cylinder Volume" template: V=πr2h. Solve for h to get h=V/(πr2). Try solving for r — the solver flags an error because r appears squared.
The Solve button is disabled until you both enter a formula and select a target variable. The selected target is underlined in yellow in the display.
Building Formulas with Buttons and Keyboard
The button panel groups inputs by type. All inputs can be made either by clicking or typing on the keyboard.
• Variable rows — an extended palette of common formula letters: x, y, A, P, V, r, h, l, w, m, b, d, t, C, F, n, a, c, R, S. Type any letter directly for variables not on the palette. • Number row — digits 0 through 9 and the decimal point. • Operator row — multiplication, division, plus, minus, equals. • Special row — π, caret operator, x2 shortcut, parentheses.
The variable palette is case-sensitive: capital A and lowercase a are treated as different variables. This matters for formulas like the simple-interest formula A=P(1+rt) where A is amount and a might be acceleration in a different context.
Keyboard shortcuts: type letters and digits directly, use star or slash for multiplication and division, type π as the Unicode character, and press Enter to solve. Ctrl+Z undoes up to fifty edits back; Backspace and Delete behave as expected. Clearing the formula also resets the target variable selection.
Try an Example — Ten Formula Templates
Click the "Try an Example" header to expand the template panel. Each card loads a real-world formula.
• Slope-Intercept — y=mx+b. Solve for m, b, or x. • Area of Rectangle — A=l⋅w. Solve for l or w. • Perimeter — P=2l+2w. Solve for l or w. • Distance — d=r⋅t. Solve for r or t. • Cylinder Volume — V=πr2h. Solve for h (linear in h) or π (linear in π). • Temperature — F=(9/5)C+32. Solve for C to get the inverse conversion. • Standard Form Line — ax+by=c. Solve for x, y, a, b, or c. • Kinematic — d=vt+(1/2)at2. Solve for v or a (linear); t is not linear. • Simple Interest — A=P(1+rt). Solve for P, r, or t. • Ohm's Law — V=IR. Solve for I or R.
These cover common formulas from algebra, geometry, physics, and finance — the typical use cases for literal equation rearrangement.
Reading the Step-by-Step Solution
The solution panel shows each algebraic move as a labeled step. The sequence depends on where the target variable appears.
• Original Equation — restates the input for reference. • Isolate the Variable — for formulas where the target has coefficient 1 (or -1) and appears alone, this step moves everything else to the other side. • Isolate the Term — for formulas where the target has a non-trivial coefficient (like V=IR solving for R), this step moves the non-target terms to the other side, leaving the coefficient-times-target on one side. • Divide Both Sides — divides by the coefficient of the target to isolate it. Produces a fraction in the result if the coefficient is not 1. • Solution — final restated answer showing target=expression.
The final-answer card at the bottom renders the result with proper fraction notation: numerator above a horizontal bar, denominator below. This makes the symbolic answer easy to read at a glance.
For identity cases (the target cancels out and both sides are equal), the solver reports "Identity". For contradictions (the target cancels but the constants do not match), it reports "No solution".
When the Solver Can and Cannot Help
The solver handles the standard linear case: the target variable appears to the first power, not inside denominators, not as part of products with itself.
Cases the solver handles.
• Simple linear — y=mx+b for any of y, m, b, x. • Multiplicative — A=lw, V=IR, d=rt. Solve for any factor. • Mixed sum and product — P=2l+2w. Each variable is linear. • With parameter expressions — V=πr2h for h (linear in h, despite the r2); A=P(1+rt) for P, r, or t.
Cases the solver flags as not linear.
• Target appears in a power — V=πr2h solved for r requires a square root, not isolated by linear moves. • Target appears in a denominator — f=1/(R1+R2) solved for R1 requires cross-multiplication first. • Target appears in two products with non-constant factors — the solver detects this and reports the equation is not linear in the target. • Target multiplied by itself — A=πr2 for r involves a square root.
For non-linear cases, manual rearrangement combining the radical-equation or quadratic-equation techniques is needed. The solver guides you to the right tool by flagging the structural issue.
For deeper coverage see rearranging formulas and symbolic manipulation.
What is a Literal Equation?
A literal equation is an equation containing two or more variables (letters representing quantities) where the relationship between them is fixed by a formula. Common examples come from every quantitative field:
• Geometry — A=lw (area of rectangle), C=2πr (circumference of circle), V=πr2h (cylinder volume). • Algebra — y=mx+b (slope-intercept form of a line), ax+by=c (standard form). • Physics — F=ma (Newton's second law), V=IR (Ohm's law), d=vt+(1/2)at2 (kinematic). • Finance — A=P(1+rt) (simple interest), A=P(1+r/n)nt (compound interest). • Conversion — F=(9/5)C+32 (Celsius to Fahrenheit).
Solving a literal equation means choosing one of the variables as the subject (the target) and rewriting the equation so that variable stands alone on one side. The result expresses the target as a function of the other variables.
The same formula can be solved for any of its variables, yielding a different rearranged form each time. For example, V=IR gives three useful forms: V=IR, I=V/R, and R=V/I.
For deeper coverage see formulas, algebraic manipulation, and changing the subject of a formula.
The Solving Process Explained
Four moves rearrange any linear literal equation. The moves are the same as for numerical linear equations, but applied symbolically.
• Move 1: Distribute brackets containing the target. If the target appears inside a bracketed expression multiplied by something else, distribute first. Example: A=P(1+rt) for r becomes A=P+Prt.
• Move 2: Collect target-containing terms. Move every term containing the target to one side and every term not containing the target to the other. Use addition or subtraction on both sides. Example: A−P=Prt after subtracting P.
• Move 3: Factor the target (if it appears in multiple terms). Pull the target out as a common factor. Example: if you had A=Prt+Pr, factor to A=Pr(t+1).
• Move 4: Divide both sides by the coefficient of the target. The coefficient is whatever multiplies the target after collecting. Example: A−P=Prt becomes r=(A−P)/(Pt).
Each move preserves the equality. Symbolic manipulation works the same as numerical manipulation: what you do to one side, you do to the other.
The solver implementation. Internally, the solver builds an expression-tree representation of the equation and computes the linear decomposition coeff⋅target+constant=0 where coeff and constant are symbolic expressions (not numbers). The solution is then target=−constant/coeff, simplified for readability.
For comprehensive treatment see solving formulas for a variable and symbolic algebra.
Related Concepts
Formula Rearrangement — the general process of changing which variable is the subject. Literal-equation solving is the algebraic technique behind it.
Linear Equations — literal equations specialized to a single unknown with concrete numerical coefficients. The solver routes through the same isolation logic.
Function Inverse — if y=f(x), solving for x in terms of y produces the inverse function x=f−1(y). Literal-equation solving is the algebraic way to find an inverse.
Symbolic Manipulation — the general field of algebraic transformations performed on expressions containing variables. Computer algebra systems perform symbolic manipulation at industrial scale; this solver does a constrained subset.
Substitution — the reverse operation. After solving A=lw for w=A/l, you can substitute the rearranged form into another formula containing w.
Slope-Intercept Form — y=mx+b. The most commonly rearranged literal equation in introductory algebra.
Quadratic Formula — an example of literal-equation rearrangement at scale: ax2+bx+c=0 solved for x in terms of a, b, c gives the quadratic formula. The result is a closed-form expression in three symbolic parameters.
Physical Formulas — many appear in textbooks in one form and must be rearranged to compute different quantities. The kinematic equation d=v0t+(1/2)at2 commonly needs rearrangement for v0 or a.
Geometry Formulas — area, volume, and surface-area formulas commonly require solving for dimensions when other quantities are given. Example: the volume of a cylinder is V=πr2h, solved for h when V and r are known.