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Ratio Calculator — Proportion & Ratio Solver

Find ratios, proportions, and scale factors

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Calculation Type

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BK
By Ben Konna, PhD

Ratio Calculator: Simplify, Scale, and Solve Proportions

Table of Contents - Ratio

Ratios in Business and Finance 2026

Ratios provide critical insights across financial analysis, investment decisions and business operations. Understanding key ratios enables informed decision-making.

Financial Health Ratios

FTSE 100 Company Metrics (February 2026):

| Company | Price-to-Earnings | Debt-to-Equity | Current Ratio | |---------|-------------------|----------------|---------------| | Shell | 8.2:1 | 0.42:1 | 1.21:1 | | AstraZeneca | 24.5:1 | 0.78:1 | 0.89:1 | | HSBC | 7.8:1 | 12.4:1 | N/A | | Unilever | 19.3:1 | 1.85:1 | 0.72:1 | | BP | 6.9:1 | 0.51:1 | 1.15:1 |

Healthy Ratio Benchmarks:

| Ratio | Healthy Range | Warning Signs | |-------|---------------|---------------| | Current Ratio | 1.5:1 to 2:1 | Less than 1:1 | | Quick Ratio | Greater than 1:1 | Less than 0.5:1 | | Debt-to-Equity | Less than 2:1 | Greater than 3:1 | | Interest Coverage | Greater than 3:1 | Less than 1.5:1 |

Property Market Ratios

UK House Price-to-Income Ratios (2026):

| Region | Ratio | Affordability Assessment | |--------|-------|--------------------------| | London | 12.8:1 | Severely unaffordable | | South East | 9.4:1 | Seriously unaffordable | | East of England | 8.7:1 | Seriously unaffordable | | UK Average | 7.2:1 | Moderately unaffordable | | North East | 5.1:1 | Moderately unaffordable | | Scotland | 5.8:1 | Moderately unaffordable |

Technology and Computing

Display Aspect Ratios (2026):

| Format | Ratio | Typical Use | |--------|-------|-------------| | Standard HD | 16:9 | Television, monitors | | Ultrawide | 21:9 | Gaming, productivity | | Super Ultrawide | 32:9 | Professional trading | | IMAX | 1.43:1 | Cinema | | CinemaScope | 2.39:1 | Widescreen films | | Mobile Portrait | 9:16 | TikTok, Instagram Stories |

The Core Principle: Proportional Relationships

A ratio compares two or more quantities by division. A proportion states that two ratios are equal.

Basic ratio: 3:4 means "3 parts to 4 parts" or "3 for every 4."

Equivalent ratios: 3:4 = 6:8 = 9:12 = 15:20. Multiplying or dividing both terms by the same number creates equivalent ratios.

Simplifying ratios: Find the Greatest Common Divisor (GCD) of both terms and divide by it. 18:24 → GCD is 6 → 3:4.

Proportions: If a:b = c:d, then a×d = b×c (cross-multiplication). This allows solving for unknown values.

Scaling: To scale a ratio up or down, multiply all terms by the same factor. 2:3 scaled by 4 becomes 8:12.

Ratios are fundamental to mixing, cooking, finance, construction and countless other applications where maintaining proportions matters.

How to Use This Calculator

Select Calculation Type:

  • Simplify — Reduce a ratio to lowest terms
  • Scale — Enlarge or reduce a ratio proportionally
  • Solve Proportion — Find a missing value in a proportion

For simplifying, enter both terms of the ratio (e.g., 18 and 24).

For scaling, enter the original ratio and the scaling factor.

For solving proportions, enter three known values to find the fourth (e.g., 5:7 = x:49).

Click "Calculate" to see results. The output displays:

  • Simplified ratio in lowest terms
  • Scaled values maintaining proportion
  • Missing value in proportions
  • Expression showing the calculation performed

How to Work with Ratios Manually

Simplifying a ratio: Find GCD and divide both terms.

Example: Simplify 48:64 Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 Factors of 64: 1, 2, 4, 8, 16, 32, 64 GCD = 16 48 ÷ 16 = 3, 64 ÷ 16 = 4 Result: 3:4

Solving a proportion: Use cross-multiplication.

Example: 5:7 = x:49 5 × 49 = 7 × x 245 = 7x x = 35 Verify: 5:7 = 35:49 (both reduce to 5:7) ✓

Scaling a ratio: Multiply all terms by the same factor.

Example: Scale 2:3:5 to make the first term 10 Factor = 10 ÷ 2 = 5 2 × 5 = 10, 3 × 5 = 15, 5 × 5 = 25 Result: 10:15:25

Converting ratio to fractions: 3:4 means 3 parts + 4 parts = 7 total parts First quantity = 3/7 of total Second quantity = 4/7 of total

Example: Split £70 in ratio 3:4 First share = £70 × 3/7 = £30 Second share = £70 × 4/7 = £40

Real-World Applications

Cooking and recipes. A recipe for 4 servings needs scaling to 10 servings. Multiply all ingredients by 10/4 = 2.5.

Mixing concrete. Cement:sand:gravel in 1:2:4 ratio. For 6 buckets of gravel: cement = 6 × (1/4) = 1.5 buckets.

Financial ratios. Debt-to-equity ratio, price-to-earnings ratio and current ratio assess company health.

Map scales. A 1:50,000 map means 1 cm represents 50,000 cm (500 m) in reality.

Architecture and design. Golden ratio (≈1:1.618) appears in aesthetically pleasing proportions.

Paint mixing. Mix colours in specific ratios: 3 parts blue to 1 part yellow creates a specific green.

Worked Calculations and Scenarios

Scenario 1: Investment Portfolio Division

Context: Dividing £150,000 inheritance in ratio 5:3:2 among three beneficiaries.

Total parts: 5 + 3 + 2 = 10

Beneficiary A: £150,000 × 5/10 = £75,000
Beneficiary B: £150,000 × 3/10 = £45,000
Beneficiary C: £150,000 × 2/10 = £30,000

Verification: £75,000 + £45,000 + £30,000 = £150,000 ✓

Scenario 2: Concrete Mixing for Patio Project

Context: Standard concrete mix ratio 1:2:3 (cement:sand:aggregate).

Project requires 12 bags of aggregate.

Aggregate = 3 parts
12 bags = 3 parts
1 part = 12 ÷ 3 = 4 bags

Cement needed: 4 × 1 = 4 bags
Sand needed: 4 × 2 = 8 bags
Aggregate: 4 × 3 = 12 bags

Total materials: 4 + 8 + 12 = 24 bags

Scenario 3: Screen Aspect Ratio Calculation

Context: Determining monitor dimensions from diagonal and aspect ratio.

Monitor: 27-inch diagonal, 16:9 aspect ratio

Using Pythagorean theorem:
Width² + Height² = Diagonal²
For 16:9 ratio: Width = 16k, Height = 9k

(16k)² + (9k)² = 27²
256k² + 81k² = 729
337k² = 729
k² = 2.163
k = 1.471

Width = 16 × 1.471 = 23.5 inches (59.7 cm)
Height = 9 × 1.471 = 13.2 inches (33.6 cm)

Scenario 4: Currency Exchange Proportion

Context: Currency conversion using exchange rate ratios (February 2026).

Exchange rate: £1 = €1.17 Converting £2,500 to euros.

Proportion: 1:1.17 = 2500:x
1 × x = 1.17 × 2500
x = 2,925

£2,500 = €2,925

Reverse conversion: €1,000 to pounds: 1.17:1 = 1000:x x = 1000 ÷ 1.17 = £854.70

Scenario 5: AI Model Parameter Scaling

Context: Large Language Model training compute ratios.

Base model parameters: 7 billion Target model: 70 billion parameters Scaling ratio: 1:10

Compute scaling (approximate square law):
Compute ratio ≈ (parameter ratio)^1.7
= 10^1.7
= 50.1

If base model requires 1,000 GPU-hours:
Scaled model requires approximately 50,100 GPU-hours

Scenario 6: Salary Distribution Analysis

Context: CEO-to-median-worker pay ratio at UK companies (2025 data).

| Company | CEO Pay | Median Worker | Ratio | |---------|---------|---------------|-------| | AstraZeneca | £15.8m | £52,400 | 302:1 | | Shell | £9.7m | £58,200 | 167:1 | | Tesco | £4.4m | £21,800 | 202:1 | | Lloyds | £5.3m | £37,600 | 141:1 |

Analysis:

FTSE 100 average ratio: 109:1
If median worker earns £35,000:
Average CEO pay = £35,000 × 109 = £3,815,000

Common Mistakes and How to Recover

Confusing ratio and fraction. A ratio 3:4 compares parts (3 to 4). A fraction 3/4 compares part to whole. Ratio 3:4 means fractions 3/7 and 4/7 of the whole.

Not converting units. 2 metres to 50 cm is not 2:50. Convert: 200 cm to 50 cm = 200:50 = 4:1.

Wrong cross-multiplication. In a:b = c:d, cross-multiply as a×d = b×c, not a×c = b×d.

Incomplete simplification. 24:36 → 4:6 is not fully simplified. Continue: 4:6 → 2:3.

Order reversal. Ratio 3:4 is different from 4:3. Maintain consistent order based on what is being compared.

Sources

FAQs

How do I simplify a ratio with decimals?

Multiply both terms by 10, 100, etc., to eliminate decimals, then find GCD. Example: 0.8:2 → 8:20 → 2:5.

Can this handle three-part ratios?

Yes. Enter ratios like 1:2:4 for concrete mix or investment allocation.

What if I only know one part of a proportion?

Enter the known ratio and one value from the second ratio. The calculator solves for the missing term using cross-multiplication.

Is a ratio the same as a fraction?

Related but different. Ratio 3:4 compares parts (3 to 4). As a fraction, it can represent 3/4 = 0.75, or the parts 3/7 and 4/7 of a whole.

How do I scale a recipe for different servings?

Find the scaling factor: new servings / original servings. Multiply all ingredient quantities by this factor.

Can I use this for aspect ratios?

Yes. Enter screen dimensions to simplify (1920:1080 → 16:9) or find equivalent dimensions.

Why does my simplified ratio have decimals?

If inputs are decimal, output may be too. Multiply to get whole numbers first, then simplify.

How do I divide an amount in a given ratio?

Sum the ratio parts, divide total amount by this sum, then multiply by each part. Example: £100 in 2:3 ratio = £100/5 = £20 per part = £40 and £60.

What is a rate versus a ratio?

A rate compares quantities with different units (miles per hour, price per pound). A ratio compares quantities with the same unit (3 apples to 4 apples). Both use the colon notation.

How do I convert a ratio to a percentage?

For ratio a:b, percentage of first = a/(a+b) × 100. Ratio 3:7 means 3/10 = 30% for first part, 70% for second.

What is direct proportion?

When one quantity increases, the other increases at the same rate. If y = kx for constant k, y and x are directly proportional.

What is inverse proportion?

When one quantity increases, the other decreases proportionally. If y = k/x for constant k, y and x are inversely proportional.

What is the golden ratio?

Approximately 1:1.618 (φ). A rectangle with these proportions is aesthetically pleasing. Found in nature, art, architecture and the Fibonacci sequence.

How do gear ratios work?

A 2:1 gear ratio means the driven gear rotates once for every two rotations of the driving gear. This trades speed for torque or vice versa.

What are financial ratios?

Metrics comparing financial statement items: debt-to-equity, current ratio, profit margin. Used to assess company health and compare across industries.