Diamond Problem Solver
Solve the classic factoring "diamond problem": find the two numbers that have a given sum and a given product.
Inputs explained
- Sum of the two numbers — The value the two unknown numbers add up to (the top of the diamond).
- Product of the two numbers — The value the two unknown numbers multiply to (the bottom of the diamond).
How to use it
- Fill in the fields above — each input has a hint describing exactly what to enter
- Press Calculate to get your result instantly, right on this page
- Copy the result, save the tool to favorites, or share and embed it anywhere
Understanding the result
Example: With sum 7 and product 12, the two numbers are 3 and 4.
Frequently asked questions
What happens if no pair of numbers has the given sum and product? If the discriminant (sum² − 4×product) is negative, no real pair exists and the calculator will indicate there's no real solution.
Can the two numbers be negative or non-integer? Yes — the diamond problem solver isn't limited to positive whole numbers; it solves the underlying quadratic, so negative or decimal answers are valid results.
Is the Diamond Problem Solver free to use? Yes — it is completely free, with no sign-up, no download and no usage limits. You can use it as often as you need.
Is my data private? Yes. The calculation runs entirely in your browser — the values you enter are never sent to our servers, stored or shared with anyone.
What information do I need? Just the following: Sum of the two numbers, Product of the two numbers. Each field includes a hint explaining exactly what to enter.
Can I use it on my phone? Yes — the tool is fully responsive and works on any device, and the same calculator is available in the EasyWorkCalcs mobile app.
Privacy
Everything you enter into the Diamond Problem Solver is processed entirely in your browser. Nothing is uploaded, stored or shared — your data stays on your device.