Ratio Calculator — Simplify & Solve

Divide an amount by a given ratio. Simplify ratios and see percentage splits.

Source: BBC Bitesize — Ratios

By Konstantin Iakovlev · Founder, Calks.uk

Last updated: April 2026 · Verified against HMRC and GOV.UK 2026/27 rates

How we calculate

Total Amount to Divide

Part A (3)

300

Part B (4)

400

Simplified ratio: 3 : 4

A is 42.9% · B is 57.1%

Disclaimer

This calculator is provided for informational purposes only and should not be considered as financial or tax advice. All calculations are performed locally in your browser — no personal data is collected or sent to our servers. Rates and thresholds are sourced from HMRC and GOV.UK and are updated for the current tax year. Always verify results with HMRC or consult a qualified professional before making financial decisions.

How It Works

A ratio compares two or more quantities. This calculator simplifies ratios to their lowest terms, scales them up or down, and solves for an unknown value in a proportion. Enter values separated by colons (e.g. 12:8) to simplify, or enter three of four values in a proportion to find the missing one.

Ratios are used in cooking (scaling recipes), construction (mixing concrete at 1:2:3), finance (price-to-earnings ratios) and map reading (1:50,000 scale). The calculator shows the GCD used for simplification and the cross-multiplication step used for solving proportions.

Simplifying ratios. Divide both sides by GCD. 12:18 → GCD 6 → 2:3. 60:36:24 → GCD 12 → 5:3:2. Euclidean algorithm: GCD(a,b) = GCD(b, a mod b). 60 mod 36 = 24; 36 mod 24 = 12; 24 mod 12 = 0 → GCD = 12. Ratios with decimals: multiply both by same factor to clear. 0.5:1.5 → ×2 → 1:3. Mixed units: convert to same unit first. 50cm:1m → 50:100 → 1:2.

UK financial ratios. LTV (Loan-to-Value) mortgage: loan ÷ property value (e.g. £160k ÷ £200k = 80% LTV). Debt-to-income: monthly debt ÷ gross monthly income. Mortgage lenders cap ~40-45% DTI. PE ratio: share price ÷ earnings per share (FTSE 100 avg ~14). Current ratio: current assets ÷ current liabilities (1.5-3 is healthy). Gearing: debt ÷ equity. Pension annuity rates: £/£1,000 (e.g. £62/year per £1,000 at age 65 = 6.2% rate).

Aspect ratios and screen sizes. Common ratios: 16:9 (TVs, monitors, YouTube), 4:3 (legacy), 21:9 (cinema, ultrawide), 1:1 (Instagram square), 9:16 (vertical phone, TikTok). 16:9 1080p = 1920×1080 pixels. 4K UHD = 3840×2160 (4× area of 1080p). Movie ratios: 1.85:1 (widescreen), 2.39:1 (anamorphic 'scope'). Photo: 3:2 (DSLR), 4:3 (compact, phone), 1:1 (medium format).

Map scales and dilution. OS Explorer 1:25,000: 1cm = 250m. OS Landranger 1:50,000: 1cm = 500m. London A-Z central: 1:8,400. Squash 1:4 = 1 part concentrate to 4 parts water. Chemicals: 1:10 dilution = 1 part in 10 total. Photography f-stops: focal length ÷ aperture diameter (f/2.8 = aperture diameter = focal length ÷ 2.8). Gear ratios: 3:1 means input wheel turns 3× per output turn.

Practical UK ratios. Cement:sand:aggregate mixing: 1:3:6 (general); 1:2:4 (medium strength); 1:1.5:3 (high strength). Paint dilution for mist coat: 1:1 with water (new plaster). Tax bracket ratios: basic 20%; higher 40% (2× basic). Pension contribution efficiency: £100 net pension costs £80 (basic rate), £60 (higher rate), £55 (additional rate). Stamp duty bands: 0%, 2%, 5%, 10%, 12% — ratios increase steeply with property value.

Example: Simplify 45:60 and scale a recipe

GCD of 45 and 60 = 15
45:60 simplifies to 3:4
Recipe calls for 200 g flour at 3:4 ratio with sugar
Sugar needed: 200 × (4/3) = 266.67 g

Source: BBC Bitesize — Ratios

Frequently Asked Questions

Simplifying ratios — finding the GCD.: Divide both sides by greatest common divisor. 12:18 → GCD is 6 → 2:3. 60:36:24 → GCD 12 → 5:3:2. Use Euclidean algorithm: GCD(a,b) = GCD(b, a mod b). 60 mod 36 = 24; 36 mod 24 = 12; 24 mod 12 = 0 → GCD = 12. Ratios with decimals/fractions: multiply both by same factor to clear decimals first. 0.5:1.5 → multiply by 2 → 1:3. Mixing units: convert to same unit first (50cm : 1m → 50:100 → 1:2).
Ratios in UK financial contexts.: Common UK financial ratios: LTV (Loan-to-Value) mortgage = loan ÷ property value (e.g. £160k / £200k = 80% LTV); debt-to-income = monthly debt payments ÷ gross income (mortgage lenders cap ~40-45%); PE ratio (FTSE 100 average ~14); current ratio (current assets ÷ current liabilities, 1.5-3 is healthy); gearing (debt ÷ equity). Pension annuity rates quoted as £ per £1,000 (e.g. £62/year per £1,000 at 65 = 6.2% rate).
Aspect ratios and screen sizes.: Common screen ratios: 16:9 (TVs, monitors, YouTube), 4:3 (legacy TVs, old computer monitors), 21:9 (cinema, ultrawide monitors), 1:1 (Instagram square), 9:16 (vertical phone video, TikTok). 16:9 1080p = 1920×1080 pixels. 4K UHD = 3840×2160 (4× area of 1080p). Movie aspect ratios: 1.85:1 (standard widescreen), 2.39:1 (anamorphic 'scope'). Photo standards: 3:2 (DSLR), 4:3 (compact, phone), 1:1 (medium format square).
Map scales and dilution ratios.: Map scale 1:25,000 (OS Explorer) = 1cm represents 250m on the ground; 1:50,000 (OS Landranger) = 1cm = 500m. London A-Z central: 1:8,400 (≈ 4 inches to 1 mile). Dilution ratios — squash 1:4 = 1 part concentrate to 4 parts water. Chemicals: 1:10 dilution means 1 part in 10 total. Photography: f-stops are ratios of focal length to aperture diameter (f/2.8 means aperture diameter = focal length ÷ 2.8). Gear ratios: 3:1 means input wheel turns 3× per output turn.