Math AI Solver: Free Step-by-Step Solutions to Any Problem
Type an equation or paste a word problem. The math solver returns every step of the solution with a reason for each one, so the next problem on your worksheet gets easier, not just this one.
This solver is part of the free AI Mathematician for tutoring and concept explanations, or jump straight into the math chat.
From Typed Problem to Explained Answer in Four Steps
Plain text works: x^2 for powers, sqrt() for roots, or an entire word problem copied from your assignment.
The problem is sent straight into the AI mathematician chat. No account, no signup screen in between.
Each line of the solution states what was done and why, in the same format as the worked examples below.
Question any step, ask for a simpler version, or request a practice problem at the same difficulty.
Three Fully Worked Problems: What Step-by-Step Actually Looks Like
Plenty of tools print an answer. The value of a step-by-step math solver is the reasoning between the problem and the answer. Here is exactly the kind of working you get back, across three common problem types.
Solve a quadratic by factoring
- Confirm the equation is in standard form ax² + bx + c = 0. It is, with a = 1, b = 2, c = -15. Because a = 1, we can factor by finding two numbers directly.
- Find two numbers that multiply to c (-15) and add to b (2). List the factor pairs of -15: (1, -15), (-1, 15), (3, -5), (-3, 5). The pair -3 and 5 multiplies to -15 and adds to 2.
- Rewrite the quadratic using those numbers as the constants in two binomials: x² + 2x - 15 = (x - 3)(x + 5).
- Apply the zero product property: if a product of factors equals zero, at least one factor must be zero. So x - 3 = 0 or x + 5 = 0.
- Solve each small equation: x = 3 or x = -5.
- Verify both answers in the original equation. For x = 3: 9 + 6 - 15 = 0. For x = -5: 25 - 10 - 15 = 0. Both check out.
Differentiate with the chain rule
- Recognize a composite function: something is raised to the 3rd power, and that something is itself a function of x. The chain rule applies whenever a function sits inside another function.
- Name the layers. Outer function: u³ (a cube). Inner function: u = 4x² - 7.
- Differentiate the outer function while leaving the inner function untouched: d/du of u³ is 3u², which gives 3(4x² - 7)².
- Differentiate the inner function on its own: d/dx of (4x² - 7) is 8x, because the derivative of 4x² is 8x and the constant -7 vanishes.
- Multiply the two results. The chain rule says f'(x) = (outer derivative) times (inner derivative): f'(x) = 3(4x² - 7)² · 8x.
- Simplify by combining the constants: f'(x) = 24x(4x² - 7)².
Translate a rate-distance problem into an equation
- Translate before calculating. Define the unknown: let t = the car's driving time in hours. The van has been driving longer, so its time is t + 0.5 hours.
- Write what "catching up" means mathematically: both vehicles have covered the same distance at that moment. Using distance = rate × time, the van's distance is 45(t + 0.5) and the car's distance is 60t.
- Set the two distances equal: 45(t + 0.5) = 60t.
- Distribute on the left side: 45t + 22.5 = 60t. The 22.5 is the van's head start in miles (45 mph for half an hour).
- Subtract 45t from both sides to collect the variable: 22.5 = 15t. The 15 here is the speed gap; the car closes the head start at 15 mph.
- Divide both sides by 15: t = 1.5 hours. Check it: the car covers 60 × 1.5 = 90 miles; the van covers 45 × 2 = 90 miles. Same distance, so the answer holds.
How to Enter Math Problems
No equation editor needed. The solver reads ordinary keyboard notation, full sentences, and everything in between. A few habits make the answers sharper.
Typing plain-text math
Use the caret for powers: x^2 means x squared, 2^10 means 2 to the 10th. Roots are sqrt(16) or sqrt(x + 3). Write fractions with a slash and parentheses: (x + 1)/(x - 2) keeps the whole numerator and denominator together, while x + 1/x - 2 would be read as four separate terms.
Other useful spellings: pi for π, |x - 4| for absolute value, log_2(8) for a log with base 2, and 3.5e8 for scientific notation.
Pasting word problems
Paste the entire problem exactly as written, including the question sentence. Do not pre-translate it into symbols; the translation step is where most word-problem mistakes happen, and the solver shows that step explicitly so you can learn it.
If the problem references a figure or table, describe it in a sentence: "the triangle has legs 6 and 8" or "the table shows values 2, 5, 9, 14 at x = 1 through 4."
Setting the explanation depth
Add one sentence about what you want back. "Show every algebra step" produces the full working. "Just verify my answer" gets a quick confirmation. "Explain this like I'm in 8th grade" simplifies the language without dumbing down the math.
This works because the model reasons through the problem one step at a time before answering, an approach known as chain-of-thought reasoning. The depth instruction controls how much of that reasoning gets written out for you.
AI Math Solver vs. Graphing Calculator vs. CAS
These three tools solve different problems, and pretending otherwise would be dishonest. A graphing calculator is the right choice when you need a fast, guaranteed-correct numeric answer or a visual: plotting y = x² - 4x to see where it crosses the axis, or checking a decimal answer during a timed exam where calculators are permitted. It never makes an arithmetic mistake, and it never explains anything either.
A computer algebra system such as Wolfram Alpha or Mathematica is the strongest pure computation engine. For exact symbolic work, a monstrous integral, a 40-digit factorization, or simplifying an expression with a dozen nested radicals, a CAS is more reliable than any AI, because it computes by algorithm rather than by reasoning. If your only goal is a certified-correct symbolic result, use a CAS.
The AI solver wins where the other two cannot compete: explanation and translation. It reads a word problem written in plain English, shows the setup as its own step, explains why each operation is legal, finds the exact line where your own attempt went wrong, and re-explains a step three different ways until it clicks. The honest workflow for important work combines them: let the AI teach you the method, then confirm the final arithmetic with a calculator or CAS, because language models can occasionally produce a confident wrong number, a failure mode known as hallucination.
Math Topics the Solver Handles
From first fractions to university coursework. Each area below lists the kind of problems the solver works through daily.
Arithmetic
Long division with remainders explained digit by digit, fraction operations with common denominators shown, percent change and reverse percentages ("the sale price is $68 after 15% off, what was the original?").
Algebra
Multi-step linear equations and inequalities, systems solved by substitution and elimination side by side, quadratics by factoring, completing the square, or the formula, plus exponent and radical simplification.
Geometry
Area and volume of composite shapes broken into parts, angle chasing with the theorems named at each step, coordinate geometry distances and midpoints, and two-column proof outlines you can adapt.
Trigonometry
Right-triangle setups with SOH-CAH-TOA applied explicitly, unit circle values derived rather than memorized, identity verification one transformation per line, and the law of sines or cosines with the ambiguous case flagged.
Calculus
Limits including L'Hopital cases, derivatives by product, quotient, and chain rule with the rule named at each application, definite integrals by substitution or parts, and related-rates problems set up from the words.
Statistics
Mean, median, and standard deviation computed with each stage visible, binomial and normal probability with the distribution choice justified, and hypothesis tests where the null, the test statistic, and the conclusion are kept separate.
Linear Algebra
Row reduction shown one elementary operation at a time, determinants by cofactor expansion, eigenvalues from the characteristic polynomial, and clear answers to "what does this matrix actually do to a vector?"
Discrete Math
Counting problems with the permutation-or-combination decision explained, induction proofs scaffolded into base case and inductive step, set operations and Venn logic, and recurrence relations unrolled term by term.
Math Solver FAQ
Straight answers about cost, steps, word problems, accuracy, and level.
More Math Help on AskAI.free
The solver is one piece of the math cluster. These pages cover the tutoring, concepts, and background that surround it.