What is the formula for percentage change?

Percentage Change = ((New − Old) / |Old|) × 100. A positive result means an increase; negative means a decrease. Example: 50 → 75 gives (25/50) × 100 = +50% increase.

What is the difference between markup and margin?

Both measure gross profit on the same transaction, but use different bases. Markup divides by cost; margin divides by selling price. Markup is always a larger percentage than margin. Example: cost $60, sell $100 → markup = 66.7%, margin = 40%.

How do I simplify a ratio?

Find the GCD (Greatest Common Divisor) of all parts and divide each part by it. For 12:18: GCD = 6. Simplified: 2:3. For 6:9:12: GCD = 3. Simplified: 2:3:4.

What is the simple interest formula?

I = P × r × t, where P = principal, r = annual rate as decimal, t = time in years. Total amount A = P + I = P(1 + rt). Example: $5,000 at 4% for 3 years. I = 5000 × 0.04 × 3 = $600.

How do I calculate a percentage discount?

Final Price = Original × (1 − Discount%/100). For $120 with 25% off: $120 × 0.75 = $90. Savings = $120 × 0.25 = $30.

Percentage & Ratio Calculators

Free online percentage and ratio calculators — from basic percent change and discount calculators to markup, margin, proportions, and interest. Every tool includes step-by-step working and a reference table.

Core Percentage Calculators

Calculate percentage change, decrease, reverse percentage, and error. These tools cover the most common percentage calculations in everyday life, science, and business.

Percentage Change Calculator

Calculate % increase or decrease between two values. Shows direction and absolute change.

Percent Decrease Calculator

((Original − New) / Original) × 100 — step-by-step working.

Reverse Percentage Calculator

Find the original value before a % was applied. Pre-tax, pre-discount prices.

Percentage Difference Calculator

Symmetric comparison: |v1−v2| / ((v1+v2)/2) × 100.

Percentage Error Calculator

|experimental − theoretical| / |theoretical| × 100. Lab measurement accuracy.

Parts Per Million Calculator

Convert between ppm, ppb, ppt, %, and mg/L.

a:b

Ratio & Proportion Tools

Simplify ratios, solve proportions, and convert between ratios, fractions, decimals, and percentages. Includes GCD-based ratio simplification with prime factorization steps.

Ratio Calculator

Simplify ratios to lowest terms, scale ratios, find equivalent ratio families.

Ratio Simplifier

Simplify 2 and 3-part ratios with prime factorization steps.

Proportion Calculator

Solve a/b = c/d for any missing value using cross-multiplication.

Ratio to Percentage Converter

Convert ratio a:b to percentage and percentage to ratio.

Fraction to Percent Calculator

(numerator/denominator) × 100. Includes common fractions table.

Decimal to Percent Calculator

Bidirectional converter: decimal ↔ percentage.

Key Percentage Formulas

Percentage Change

((New − Old) / |Old|) × 100

Percent Decrease

((Original − New) / Original) × 100

Reverse Percentage (increase)

Original = Value / (1 + Rate/100)

Markup %

((Selling − Cost) / Cost) × 100

Gross Margin %

((Selling − Cost) / Selling) × 100

Simple Interest

I = P × r × t

Business & Finance

Practical business and financial percentage tools: markup, margin, discounts, tips, tax, and simple interest. All tools distinguish related concepts (markup vs margin, discount vs reduction).

Markup Calculator

((Selling − Cost) / Cost) × 100. Find markup % or calculate selling price.

Margin Calculator

((Selling − Cost) / Selling) × 100. Gross profit margin from cost and price.

Discount Calculator

Sale price from discount %. Also find what % discount was applied.

Tip Percentage Calculator

Tip amount with 15/18/20/25% presets. Split bill among N people.

Tax Percentage Calculator

Add tax to price or find pre-tax amount. US state presets (CA, NY, TX, FL).

Simple Interest Calculator

I = P × r × t with year-by-year breakdown table.

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Formula Guides

In-depth guides with derivations, worked examples, and industry benchmarks.

Compound Interest Formula Explained

A = P(1+r/n)^(nt) — derivation, variables, Rule of 72, continuous compounding.

APR Formula Breakdown

APR vs APY, loan rate calculation, credit card APR, nominal vs effective rate.

Profit Margin Formula

Gross, net, and operating margin — formulas, benchmarks, and worked examples.

A↔B

Comparisons

Side-by-side comparisons to clarify commonly confused concepts.

Percentage vs Percentile

% is a ratio out of 100; percentile is a rank. Test scores, growth charts, income.

Markup vs Margin

Same gross profit, different bases. Decision table and conversion formulas.

Simple vs Compound Interest

I=Prt vs A=P(1+r/n)^(nt). $10K at 5% over 30 years data table.

Ratio vs Proportion

A ratio compares; a proportion states two ratios are equal. When to use each.

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Frequently Asked Questions

Educational use only. All calculators use standard mathematical formulas. For professional financial, accounting, or scientific applications, verify results with authoritative references. Tax rates and financial benchmarks are approximate and may change. Last updated: March 2026.