◆ Free Online Tool

Solve Any Diamond Problem Instantly

Enter any two values in the diamond — get the other two numbers immediately with a full step-by-step explanation. Supports negatives, decimals, and all problem types.

Product (×) 12 Sum (+) 7 A 3 B 4

Everything you need to solve diamond problems

Built for algebra students — fast, clear, and completely free.

Instant Results

Enter any two diamond values and get the missing pair in milliseconds — no waiting, no page reloads.

±

Negatives & Decimals

Fully supports negative numbers, decimals, and fractions. Sign rules are applied automatically.

📋

Step-by-Step

See every step of the solution explained clearly — perfect for checking homework or learning the method.

Learn the method

In-depth guides to understanding and solving diamond problems.

Frequently Asked Questions

Everything you need to know about diamond problems and this solver.

A diamond problem is an algebra exercise shown as a four-cell diamond shape. The top cell holds the product of two unknown numbers (A×B), the bottom cell holds their sum (A+B), and students must find the two numbers A and B that go on the left and right sides.
(1) Identify which two values are given. (2) Apply sign rules to determine the signs of the unknowns. (3) List factor pairs of the product with the correct signs. (4) Find the pair that adds to the given sum. (5) Verify — the two numbers must satisfy both the product and sum cells.
Yes. The solver fully supports negative numbers, decimals, and fractions. Sign rules are applied automatically so you always get the correct signs for both unknown values — no manual rule-checking needed.
Yes — completely free, no registration required. Enter any two diamond values and get the other two instantly with a full step-by-step explanation showing every calculation.
Diamond problems build the exact skill needed to factor quadratic trinomials. To factor x² + 7x + 12, you need two numbers that multiply to 12 and add to 7 — which is exactly what a diamond problem asks. Mastering diamond problems makes factoring quadratics significantly faster.

Ready to solve your diamond problem?

Open the free solver — enter any two values and get the complete solution with steps shown.

◆ Open Free Solver →