Education
Simplify Calculator
Last updated: June 19, 2026
A simplify calculator is a comprehensive math utility designed to reduce algebraic and arithmetic expressions to their simplest form. The tool simplifies proper and improper fractions by dividing the numerator and denominator by their greatest common divisor, reduces ratios, and simplifies radical expressions by extracting perfect-square factors from inside square roots. Students, teachers, and professionals use this calculator to check math homework, verify algebraic solutions, and present clean mathematical values.
Pick a mode and enter your numbers. The tool reduces fractions using GCD, simplifies square roots by extracting perfect-square factors, and reduces ratios by their greatest common divisor.
Quick Answer
Reduce fractions, radicals, and ratios to their simplest forms. Enter your expression to calculate the simplified mathematical value.
e.g. 18
e.g. 24
Scope
This tool simplifies fractions (using GCD), square roots (pulling out perfect-square factors), and integer ratios. It is not a full symbolic algebra system; for full algebraic simplification (variables, polynomials, complex expressions), use a computer algebra system like Wolfram Alpha or SymPy.
Simplified fraction
3 / 4
Decimal 0.75
Fractions are reduced by dividing by GCD(numerator, denominator). Square roots are simplified by extracting all perfect-square factors. Ratios are reduced by dividing every part by the GCD of the whole list.
Examples
18 / 24
GCD 6 · simplified 3/4 · 0.75
√72
6√2 · ≈ 8.485
12 : 18
GCD 6 · reduced 2 : 3
12 : 18 : 24
reduced 2 : 3 : 4
How it works
All three modes use the Euclidean algorithm to find the GCD, then divide. The square-root mode scans for perfect-square factors up to √n.
Fraction · divide numerator and denominator by GCD
Square root · √(a² × b) = a × √b
Ratio · divide every part by GCD of all parts
Related calculators
- Fraction calculator for adding, subtracting, multiplying, and dividing fractions.
- Square root calculator for decimal and simplified square roots.
- GCF calculator for the greatest common factor of any set of numbers.
- LCM calculator for the least common multiple.
- All education calculators.
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Frequently asked questions
Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by that GCD. For example, 18/24 has GCD 6, giving 3/4. The simplified form is unique (up to sign): a fraction is in lowest terms when GCD = 1.
Factor the radicand into a product of a perfect square and a remainder. For example, √72 = √(36 × 2) = 6√2. The calculator pulls out every perfect-square factor automatically, leaving the smallest possible number under the radical.
Find the GCD of all parts of the ratio, then divide each part by that GCD. For example, 12:18 has GCD 6, giving 2:3. The same procedure works for ratios with more than two parts: 12:18:24 has GCD 6, giving 2:3:4.
No. This is a numeric simplifier, not a computer algebra system. For symbolic simplification (combining like terms, factoring polynomials, simplifying rational expressions with variables), use a CAS such as Wolfram Alpha, SymPy, or a similar tool.
Decimals aren't in scope here. Convert the decimal to a fraction first (move the decimal point and reduce), then use this calculator's fraction mode. For repeating decimals, use a fraction-from-decimal converter.
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