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Diamond Problem Solver

Result

04
13
↗ Math

Diamond Problem Solver The Diamond Problem Solver finds two numbers given their product and sum — the core of the factoring diamond method. Enter the product (top) and sum (bottom). — free online calculator.

Formula

Rule: For numbers with Sum = S and Product = P, solve t² − S·t + P = 0, so the pair is (S ± √(S²−4P))/2 when the discriminant is nonnegative.
  • Diamond Problem Solver calculates its result from Sum, Product. It uses the formula Calculated with the verified ST Calculator runtime.. Change any input to recalculate the result instantly.
  • The main inputs are Sum, Product. Enter them in the units and format shown in the calculator.
  • Keep comparable quantities in compatible units whenever the formula combines or compares them.
  • Changing any input above recalculates the result with the same calculation engine used by this page.

Example: Diamond Problem Solver

Inputs
  • Sum: 7
  • Product: 12

Using Sum = 7, Product = 12, the calculated result is [4, 3].

Sample result: Calculating…

Frequently asked questions

What does the Diamond Problem Solver calculate?

Diamond Problem Solver The Diamond Problem Solver finds two numbers given their product and sum — the core of the factoring diamond method. Enter the product (top) and sum (bottom). — free online calculator.

Which values should I enter?

Enter Sum, Product using the units and format shown beside each field.

What formula does this calculator use?

The calculator uses the following relationship: Rule: For numbers with Sum = S and Product = P, solve t² − S·t + P = 0, so the pair is (S ± √(S²−4P))/2 when the discriminant is nonnegative..

Why might my result differ from another source?

Results can differ when another source uses different units, rounding rules, conventions or assumptions. Compare the inputs and definitions before comparing results.

Does the result update automatically?

Yes. Changing an input updates the result using the same calculation engine shown on this page.

Page information

Updated: October 7, 2026