How we check answers

We'd rather say not sure than be wrong.

Any tool can print an answer. What matters is whether you can trust it. This page explains exactly what we check, how we check it, and where checking stops.

What "Verified" means

When you see a Verified stamp, it means two things happened:

1. We solved your problem.
2. We then checked the final answer with a second, independent method, and it passed.

"Independent" is the important word. Running the same calculation twice would just repeat any mistake, so we never let a solver check its own work. Instead we use a different route to the same fact — for example, putting the answer back into the question.

The stamp always says which method we used, so you can see what was checked:

• Verified · checked by substitution
• Verified · checked numerically
• Verified · checked with finite differences
• Verified · checked by differentiating back

Tap the stamp to see the details of the check.

Where we can, we check the working too, not just the answer: each line of working should be equal to the line before it. If a step fails that check, we don't show it as if it were fine.

How we check each type of problem

Equations and roots: substitution

We put each solution back into the original equation and make sure both sides come out equal (allowing only for tiny rounding in decimals). We also make sure we haven't missed or added a solution.

For example, the solutions of 2x² − 7x + 3 = 0 are x = ½ and x = 3. Putting x = ½ back in gives ½ − 3½ + 3 = 0, and x = 3 gives 18 − 21 + 3 = 0. Both work, so the stamp reads Verified · checked by substitution.

The same check is used for simultaneous equations and for the end points of inequalities.

Simplifying, expanding and identities: numerical comparison

If two expressions really are equal, they give the same value whatever number you put in. So we pick a set of test points (usually 12), work out both expressions at each one, and compare. We skip any point where an expression isn't defined.

For example, (x² − 1) ÷ (x − 1) simplifies to x + 1. We test points such as x = 0.37 and x = −2.6, but never x = 1, where the original expression has no value. A wrong simplification is very unlikely to match at a dozen random points.

The stamp reads Verified · checked numerically, and may say how many points were tested, such as "checked numerically at 12 points".

For factorising, we multiply the factors back out and compare with what you started with: checked by expanding.

Derivatives: finite differences

A derivative tells you how steep a graph is. So we measure the steepness of the original function directly — by looking at how much it changes over a tiny step either side of several points — and compare that with what our derivative formula says.

If they agree at every point, the stamp reads Verified · checked with finite differences.

Integrals: differentiating back

Integrating and differentiating undo each other. So we differentiate our answer and check that it gives back the function you started with. Answers are allowed to differ by a constant, which is why integrals end with "+ C".

For example, if we say the integral of 2x cos(x²) is sin(x²) + C, differentiating sin(x²) gives 2x cos(x²) again. The stamp reads Verified · checked by differentiating back.

For definite integrals (with limits), we also work out the area numerically and compare: checked numerically.

Limits: approaching from both sides

We work out the expression at points closer and closer to the value from the left and from the right, and check that both sides head towards our answer: checked numerically from both sides.

Fractions and long division: exact arithmetic

Here we never use rounded decimals. We redo the calculation with exact whole numbers and fractions.

For long division, we check that quotient × divisor + remainder gives back the number you started with. For example, 1234 ÷ 7 = 176 remainder 2, and 176 × 7 + 2 = 1234. The stamp reads Verified · checked with exact arithmetic.

Statistics: a second formula

Many statistics can be worked out in more than one way. We calculate them again with a different formula and make sure the results match. For example, we work out the variance from each value's distance to the mean, and again from the mean of the squares. The stamp reads Verified · checked two ways.

The four stamps

Every answer gets exactly one of these.

Verified

The answer passed an independent check. The stamp names the method.

Partial

You'll see: Answer checked · setup not independently verified.

This is common for word problems. We can check that the equations were solved correctly, but a computer can't be sure the equations are the right way to describe the story in the question. Read the setup yourself.

Not independently verified

You'll see: Not independently verified — look twice.

We couldn't check this answer. That might be because it's a proof or a sketch, the question is open-ended, or the check didn't finish in time. The answer may well be right, but treat it with care.

Failed

Sometimes a check runs and the answer doesn't pass. When that happens to an AI answer, we try again with a second AI model. If the answer still doesn't pass, we tell you plainly: We couldn't confirm this answer. Where our calculator got its own result, we show that next to it so you can compare.

A failed answer never gets a Verified stamp, and we log it automatically so we can look into it.

The problem we read

Next to every answer we show: For the problem we read, followed by the problem as we understood it, and a link: Not what you meant? Edit.

We always show this because a check can only prove that we solved the problem we read. If a photo was misread, or typed input was understood differently from what you meant, a Verified stamp would be correct about the wrong problem. Seeing the problem we read lets you catch that straight away.

To fix it: tap Edit, correct the problem, and solve again. With photos, we also show you what we read before we solve anything, so you can fix it first.

When input could mean two things, we say so. For example, 2sinx^2 could mean 2·sin(x²) or 2·(sin x)². We tell you which reading we used — such as "We read this as 2·sin(x²)" — and give you one tap to switch. Brackets always help: 2*sin(x^2) leaves no doubt.

What we can't check

We'd rather be clear about the limits than hide them.

• Word problems. We can check the maths, but not whether the equations match the story. These answers are marked Partial.
• Proofs. Whether an argument is complete and correct is very hard for a computer to confirm. Proofs are marked Not independently verified.
• Graph sketching. We don't check sketches of graphs, or how they are labelled.
• Ambiguous input. We can only check the answer to the problem we read, not the one you had in mind. That's why the problem we read is always on screen.
• How your teacher wants it set out. Verified means the answer is right. It doesn't mean the working is laid out the way your school or exam board expects.

How accurate are we?

Before any calculator goes live, it has to pass a set of test problems with known answers. That set includes deliberately wrong answers — a wrong root, a derivative with one sign flipped, an integral with one wrong term — which our checks must catch.

We are a new service, so we don't yet have real-world figures we'd be comfortable quoting, and we won't make one up. After launch, we will publish our test results every month: how often each type of problem is solved and checked correctly, and how many reported mistakes we have fixed.

Report a mistake

Every answer has a Report a mistake button. Please use it whenever something looks wrong, even if you're not sure.

A report sends us the problem as we read it and the answer we gave. It does not include your photo. You can add a short note, but please don't include your name or anyone else's.

We read reports every week. When we fix a mistake, we add that problem to our tests so the same error is caught in future.

Last updated 8 October 2026.