Solve missing ratio values, simplify ratios to their lowest terms, scale aspect ratios like 16:9, or split an amount by ratio.
Solves equivalent fractions A/B = C/X by cross-multiplying: X = (B × C) / A.
Finds the Greatest Common Divisor (GCD) of multi-part ratios to simplify terms to integers.
Resizes image and video dimensions (e.g. 16:9, 4:3) maintaining identical visual proportions.
Splits a monetary sum or quantity proportionally across multiple ratio shares: Share_A = Total × (A / Sum).
Learn how ratios express relationships between quantities, how to solve proportions using cross-multiplication, and how to scale image resolutions or recipes accurately.
A ratio compares the relative sizes of two or more numerical values. Expressed as A:B, A/B, or "A to B", it indicates how many times one number contains another.
A proportion is a statement that two ratios are equal (A:B = C:D). When three values are known, the unknown target X is calculated via cross-multiplication.
Ratios are simplified by dividing all numbers by their Greatest Common Divisor (GCD). For example, 12:18:24 reduces to 2:3:4 when divided by 6.
Goal: Find unknown value X in equivalent ratio.
Goal: Share a total amount proportionally.
Scale recipe ingredient quantities accurately when increasing or decreasing serving sizes without altering flavor profiles.
Convert blueprint scale dimensions (e.g. 1:50 or 1:100 scale) into actual real-world meters or feet accurately.
Maintain 16:9, 4:3, or 21:9 image and video aspect ratios to avoid stretching or letterboxing distortion.
Analyze financial leverage ratios like Debt-to-Equity (D/E), profit sharing ratios, and investment portfolio splits.
Ratio and proportion formulas divide a total quantity into proportional parts based on specified ratio terms or test equality between two fractions (a/b = c/d).
A proportion A:B = C:X is solved by cross-multiplication: A x X = B x C, so X = (B x C) / A. For example, in 2:3 = 10:X, X = (3 x 10) / 2 = 15.
A ratio is simplified to its lowest terms by dividing every term by their greatest common divisor (GCD). The ratio 4:6 has a GCD of 2, so it simplifies to 2:3, and this same GCD method extends to three-term ratios such as 4:6:8, which simplifies to 2:3:4.
To split a total amount by a ratio such as 2:3:5, add the parts together (2 + 3 + 5 = 10 parts) and divide the total by that sum to find the value of one part. For a total of 1,000 split 2:3:5, one part equals 100, giving shares of 200, 300, and 500.
Use the Fraction Calculator when a ratio needs to be added to or compared against a fraction, and the LCM & HCF Calculator when you need the underlying common divisor or multiple used to simplify or scale a ratio.
Quick answers about how this tool works.
Add the ratio parts (2 + 3 + 5 = 10 parts). Divide the total amount by 10 to find 1 part value, then multiply each ratio number by the 1 part value.
A ratio compares the relative sizes of two or more values. To simplify a ratio, divide all numbers by their greatest common divisor (GCD). For example, 15:20 simplifies to 3:4.
Sum the parts of the ratio to get the total parts. Divide the number by the total parts to find the value of one part, then multiply by each ratio term.
The golden ratio is a special mathematical ratio of approximately 1:1.618 (phi), widely used in art, architecture, and design for aesthetic proportions.
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