Ratio Calculator
A Ratio Calculator is a tool that solves proportions, simplifies ratios, finds missing values, and scales quantities in real time. Ratio Calculator covers ratio scaling, aspect ratio conversion, golden ratio computation, percentage-to-ratio conversion, and fraction conversion — with step-by-step solutions and visual feedback for every calculation.
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What is Ratio?
A ratio is a comparison between two or more quantities that shows how much of one thing exists relative to another. Ratios are expressed as A : B, where A and B represent the quantities being compared. For example, a ratio of 2 : 3 means for every 2 parts of the first quantity, there are 3 parts of the second quantity.
Ratios appear in math, science, finance, cooking, construction, and design. The ratio concept connects directly to fractions, proportions, and percentages — a ratio of 1 : 4 equals 1/4 as a fraction, 0.25 as a decimal, and 25% as a percentage.
Ratio Formula
The ratio formula expresses the relationship between two quantities A and B as:
To simplify a ratio, divide both terms by their Greatest Common Divisor (GCD). For instance, the ratio 12 : 8 simplifies to 3 : 2 because the GCD of 12 and 8 is 4.
The cross-multiplication method solves for a missing ratio value. Given A : B = C : X, then X = (B × C) / A. This equation forms the basis of proportion solving in this Ratio Calculator.
How to Use This Calculator
To use this Ratio Calculator, follow 3 steps:
Enter Values
Type the known ratio values into the input fields. Leave one field empty — that is the unknown value the Ratio Calculator solves.
Choose Mode
Select the ratio mode — Solve, Simplify, or Scale. Each mode applies different equations to your input values.
Get Results
Click Calculate. The result screen displays the answer with a visual ratio bar, pie chart, and step-by-step solution breakdown.
How This Calculator Works
This Ratio Calculator processes input through 4 stages: parsing, validation, computation, and display. The computation engine uses cross-multiplication to solve for the missing ratio value, GCD-based simplification to simplify ratios, and scalar multiplication to scale values.
In Solve mode, the calculator identifies which of the 4 values is missing, then applies the cross-multiplication formula. In Simplify mode, the calculator divides both terms by GCD to simplify ratios to their lowest terms. In Scale mode, it multiplies both terms by the scale factor.
Formula & Equations Used
This Ratio Calculator uses 5 core equations:
1Cross-Multiplication (Proportion Solving)▼
Cross-multiplication solves for any missing value in a proportion. Given 3 known values, the formula isolates the unknown by multiplying diagonally and dividing.
2GCD Simplification▼
The Greatest Common Divisor (GCD) reduces a ratio to its simplest form. For example, 24 : 36 → GCD is 12 → simplified to 2 : 3.
3Ratio to Percentage▼
This equation converts a ratio into its percentage representation. A ratio of 3 : 7 becomes 30% and 70%.
4Ratio Scaling▼
Scaling multiplies both terms by the same factor, preserving the proportion. A ratio of 2 : 5 scaled by 4 becomes 8 : 20.
5Ratio to Fraction / Decimal▼
Any ratio converts directly to a fraction and decimal. The ratio 3 : 4 equals the fraction 3/4 and the decimal 0.75.
Example Problems & Step-by-Step Solutions
Here are 3 example problems with step-by-step solutions using this Ratio Calculator:
Example 1Solve for X in 3 : 5 = 9 : X
Example 2Simplify the ratio 48 : 36
Example 3Scale 2 : 7 by a factor of 6
Ratio Scaling Calculator
The Ratio Scaling Calculator multiplies both terms of a ratio by the same factor to produce an equivalent ratio at a different scale. This tool is used in recipe scaling, map distances, model building, and industrial production calculations.
Aspect Ratio Calculator
An Aspect Ratio Calculator converts between screen and video dimensions. Typical aspect ratios include 16:9 (widescreen displays and YouTube videos), 4:3 (classic TV and presentations), 21:9 (ultrawide monitors), and 1:1 (square social media posts). Sizes of screens and videos depend on aspect ratio — a 1920×1080 display uses a 16:9 ratio.
Golden Ratio Calculator
The Golden Ratio equals approximately 1.6180339887 (often represented by the Greek letter phi φ). The Golden Ratio Calculator computes golden ratio values: given one side of a golden rectangle, the calculator finds the other side by multiplying or dividing by φ (1.618).
The golden ratio appears in architecture, art composition, logo design, and natural patterns (shell spirals, flower petals, leaf arrangements).
Percentage to Ratio
To convert a percentage to a ratio, place the percentage over 100, then simplify the fraction. 75% becomes 75/100, which simplifies to 3/4, giving a ratio of 3 : 4. This Ratio Calculator handles ratio-to-percentage conversion in both directions.
Evaluate Equivalent Ratios
Equivalent ratios are ratios that represent the same proportion. The ratios 2 : 3, 4 : 6, 6 : 9, and 8 : 12 are all equivalent because each simplifies to 2 : 3. To evaluate equivalent ratios, simplify both ratios to their lowest terms and compare.
Scale Ratio Calculator
A Scale Ratio Calculator converts between real-world measurements and scaled representations. This calculator is common in architecture (1:100 floor plans), model building (1:24 model cars), and cartography (1:50000 maps).
To calculate the scaled value, divide the real measurement by the scale factor. A 12-meter (39.37 ft) wall at 1:100 scale measures 12 centimeters (4.72 inches) on the plan.
Divide by Ratio Calculator
The Divide by Ratio Calculator splits a total amount into parts based on a given ratio. To divide 120 in the ratio 2 : 3, calculate the total parts (2 + 3 = 5), then assign each portion: Part A = 120 × (2/5) = 48 and Part B = 120 × (3/5) = 72.
Practical Example: Concrete Mix Ratios
Concrete Mix Ratios define the proportion of cement, sand, and gravel before mixing solutions. A standard concrete mix uses a 1 : 2 : 3 ratio — 1 part cement, 2 parts sand, 3 parts gravel. For 1 cubic meter (35.31 cubic feet) of standard concrete, this mix requires approximately 300 kilograms (661.39 pounds) of cement, 600 kg (1322.77 lbs) of sand, and 900 kg (1984.16 lbs) of gravel.
Practical Example: Scaling a Recipe
Scaling a recipe applies the Ratio Calculator to cooking. A cookie recipe calls for flour, sugar, and butter in a ratio of 3 : 2 : 1. When blending spices or adjusting portion counts, multiply each ingredient by the same scale factor to maintain the correct proportions.
Convert Ratio to Fraction
To convert ratio to fraction, write each part of the ratio as a fraction of the total. The ratio 3 : 5 converts to the fractions 3/8 and 5/8, because the total is 3 + 5 = 8 parts. The first term represents 3/8 (0.375 or 37.5%) and the second term represents 5/8 (0.625 or 62.5%).
Frequently Asked Questions
How to calculate debt to income ratio?▼
To calculate Debt-to-Income (DTI) ratio, divide total monthly debt payments by gross monthly income, then multiply by 100. The DTI ratio formula is: DTI = (Total Monthly Debts / Gross Monthly Income) × 100. A monthly debt of $1,500 with a gross income of $5,000 gives a DTI of 30%. Lenders consider a DTI below 36% favorable and above 43% risky for mortgage approval.
How to calculate for ratio?▼
To calculate a ratio between two numbers, divide both numbers by their Greatest Common Divisor (GCD). For 150 and 200, the GCD is 50, so 150/50 : 200/50 = 3 : 4. Use this Ratio Calculator by entering both values in the Simplify mode to get the reduced ratio instantly.
How to calculate cholesterol ratio?▼
To calculate cholesterol ratio, divide total cholesterol by HDL (high-density lipoprotein) cholesterol. The formula is: Cholesterol Ratio = Total Cholesterol / HDL Cholesterol. A total cholesterol of 200 mg/dL (5.17 mmol/L) with HDL of 50 mg/dL (1.29 mmol/L) gives a ratio of 4.0. Medical professionals recommend a cholesterol ratio below 5.0, with an optimal ratio under 3.5.
How can I calculate my body fat ratio?▼
To calculate body fat ratio, divide body fat mass by total body weight and multiply by 100. The formula is: Body Fat % = (Fat Mass / Total Body Weight) × 100. A person weighing 80 kg (176.37 lbs) with 16 kg (35.27 lbs) of fat has a body fat ratio of 20%. Common measurement methods include skinfold calipers, bioelectrical impedance scales, and DEXA scans.
How to calculate LTV ratio?▼
To calculate Loan-to-Value (LTV) ratio, divide the loan amount by the appraised property value and multiply by 100. The LTV formula is: LTV = (Loan Amount / Appraised Property Value) × 100. A $180,000 loan on a $225,000 property gives an LTV of 80%. An LTV above 80% typically requires Private Mortgage Insurance (PMI).
How to calculate debt coverage ratio?▼
To calculate Debt Service Coverage Ratio (DSCR), divide net operating income by total debt service. The DSCR formula is: DSCR = Net Operating Income / Total Debt Service. A business with $500,000 net operating income and $400,000 annual debt payments has a DSCR of 1.25. A DSCR above 1.0 means the business generates enough income to cover debt obligations.
How to calculate gear ratio?▼
To calculate gear ratio, divide the number of teeth on the driven gear by the number of teeth on the driving gear. The gear ratio formula is: Gear Ratio = Teeth on Driven Gear / Teeth on Driving Gear. A driven gear with 60 teeth meshed with a driving gear of 20 teeth produces a gear ratio of 3:1. This means the driving gear rotates 3 times for every 1 rotation of the driven gear, increasing torque by a factor of 3. For asymmetric gear ratios, each mesh stage is calculated separately and multiplied for the total compound ratio.