Percentage / Ratio / Average Calculator

Percentages: Parts Out of 100

A percentage is simply a way to express "how much out of 100" something represents. The word "percent" literally means "per hundred." For example, 25% means 25 out of 100, which equals 0.25 as a decimal or ¼ as a fraction.

Three classic percentage questions:

• "What is P% of W?" — Finding a part when you know the percent and whole (e.g., "What is 15% of $200?")
• "P is what percent of W?" — Finding the percent when you know part and whole (e.g., "30 is what percent of 150?")
• "Percent change from old to new?" — Measuring increase or decrease (e.g., "Growth from 100 to 125 is what percent?")

Everyday examples include discounts ("Save 20%!"), tips (leaving 18% at a restaurant), interest rates (earning 3% annually), test scores (getting 85% correct), and completion rates (finishing 60% of a project).

Ratios: Comparing Two or More Quantities

A ratio compares the size of two or more quantities, typically written as A:B (read as "A to B"). Ratios show relative size without specifying exact amounts. For example, a 2:3 ratio of red to blue marbles means for every 2 red marbles, there are 3 blue ones—but the actual counts could be 2 and 3, or 20 and 30, or 200 and 300.

• Simplifying ratios: Divide both sides by their greatest common divisor (GCD). Example: 10:15 → 2:3
• Ratios vs fractions: A:B can be viewed as the fraction A/B, but ratios emphasize comparison rather than "part of a whole"
• Scaling ratios: Multiply or divide both sides by the same number to maintain the proportion while changing total size (e.g., 2:3 → 4:6 → 20:30)

Everyday examples include recipes (2 cups flour to 1 cup water), map scales (1:50,000 means 1 cm on map = 50,000 cm in reality), mixing instructions (paint ratios, fuel mixtures), and team allocations (dividing resources 3:2:1 among departments).

Averages: Summarizing a Set of Values

An average (or mean) summarizes a set of numbers by finding their central, typical value. The simple arithmetic mean adds all values and divides by how many there are: Mean = (x₁ + x₂ + ... + xₙ) / n.

A weighted average recognizes that some values matter more than others. Each value is multiplied by its weight (importance factor) before averaging. This is essential when calculating grade point averages (where a final exam might count for 40% while quizzes count for 10% each) or when different data points represent different sample sizes.

Everyday examples include grade point averages (combining scores from different assignments), average monthly expenses (totaling spending over 12 months and dividing by 12), average test scores (class or personal performance), typical daily steps (fitness tracking), and mean customer ratings (summarizing reviews).

Percent Change: Measuring Growth or Decline

Percent change (also called percent increase/decrease or growth rate) shows how much something changed relative to its starting value. It answers questions like "Sales increased by what percent?" or "The price dropped by what percent?"

Basic formula: Percent change = [(New value − Old value) / Old value] × 100%

• Positive result: Indicates an increase (growth)
• Negative result: Indicates a decrease (decline)
• Key insight: Always divide by the original (old) value, not the new one

This concept is crucial for reading charts and graphs, understanding news reports about economic indicators, tracking business KPIs, analyzing investment returns, and measuring personal progress toward goals.

Mode 1 — Basic Percentage ("What is X% of Y?")

1. Choose the "Percentage" or "What is X% of Y?" mode
2. Enter the percent value (e.g., 18)
3. Enter the whole/base value (e.g., 250)
4. Click Calculate
5. Review the result (e.g., "18% of 250 = 45")

Use this mode when: Computing discounts, tips, commissions, or any partial amount of a total.

Example: "A $80 jacket has 30% off. How much is the discount?" → 30% of 80 = $24 discount

Mode 2 — Percent of Total ("X is what percent of Y?")

1. Choose the "X is what percent of Y?" mode
2. Enter the part (e.g., 40)
3. Enter the whole (e.g., 80)
4. Click Calculate
5. Review the result (e.g., "40 is 50% of 80")

Use this mode when: Finding percent scores, completion rates, contributions, or any time you're expressing a part relative to a whole.

Example: "I answered 42 out of 50 questions correctly. What's my score?" → 42 is 84% of 50

Mode 3 — Percent Change (Increase/Decrease)

1. Choose the "Percent Change" mode
2. Enter the old value (original amount, e.g., 120)
3. Enter the new value (current amount, e.g., 180)
4. Click Calculate
5. Review the result (e.g., "Change = +50%" indicating a 50% increase)

Use this mode when: Tracking growth, price changes, performance improvements, or any comparison between two time periods.

Example: "Monthly sales went from $10,000 to $12,500. What's the growth?" → +25% increase

Mode 4 — Ratio Simplifier and Scaler

1. Choose the "Ratio" mode
2. Enter two numbers representing the ratio (e.g., 10 and 15)
3. Click Simplify or Calculate
4. Review the simplified ratio (e.g., "2:3") and equivalent forms
5. (Optional) Enter a desired total or target value to scale the ratio

Use this mode when: Working with recipes, map scales, mixing ratios, class allocations, or any proportional division.

Example: "A recipe uses 4 cups flour to 6 cups liquid. Simplify." → 2:3 ratio

Mode 5 — Average / Weighted Average

1. Choose the "Average" or "Weighted Average" mode
2. Enter a list of numbers (e.g., test scores, monthly amounts)
3. For weighted average, also enter weights for each value (e.g., percentages or importance factors)
4. Click Calculate
5. Review the simple or weighted average and any helpful summaries

Use this mode when: Computing grade point averages, finding typical values over time, or summarizing performance scores.

Example: "My test scores are 85, 90, and 78. What's my average?" → (85+90+78)/3 = 84.3

Percentage-of Formula

To find P% of W:

1. Convert P% to decimal: p = P ÷ 100
2. Compute: result = p × W

"What Percent" Formula

To find what percent P is of W:

Percent Change Formula

Given Old and New values:

Ratio Simplification

Given ratio A:B:

1. Find greatest common divisor (GCD) of A and B
2. Simplified ratio = (A ÷ GCD) : (B ÷ GCD)

Simple Average (Mean)

Given numbers x₁, x₂, ..., xₙ:

Weighted Average

Given values v₁, v₂, ..., vₙ with weights w₁, w₂, ..., wₙ:

1. Shopping & Discounts

Situation: You see a jacket for $80 with a "30% off" sign, but want to know the exact discount amount and final price.

How you use it: Enter 30% of 80 in percentage mode. Calculator shows $24 discount. Subtract from $80 to get $56 final price.

Outcome: Instant clarity on whether the deal fits your budget, without mental math or guessing.

2. Tracking Grade Averages

Situation: A student has scores from quizzes (75, 82, 88), homework (90), and exams (78, 85). Each category has different weights: quizzes 20%, homework 20%, exams 60%.

How they use it: Calculate simple average for each category, then use weighted average mode with the three category averages and their weights.

Outcome: Clear overall grade (e.g., 82.3) and insight into where improvement matters most (exams carry the most weight).

3. Comparing Performance at Work

Situation: A manager sees last month's sales were $45,000 and this month's are $54,000. They need to report the growth rate.

How they use it: Use percent change mode with 45,000 as old value and 54,000 as new value.

Outcome: Clear report: "Sales increased 20% month-over-month," much more meaningful than just saying "$9,000 increase."

4. Recipe and Mixing Ratios

Situation: A drink mix recipe calls for syrup and water in a 1:4 ratio, but you want to make a larger batch totaling 1,000ml.

How you use it: Use ratio mode to scale 1:4 to a total of 1,000ml. Calculator shows 200ml syrup and 800ml water.

Outcome: Perfect proportions maintained, no matter the batch size. Works for cooking, painting, chemical dilutions, and more.

5. Data Summaries for School Projects

Situation: A student surveyed 50 classmates about favorite lunch options: 30 chose pizza, 12 chose sandwiches, 8 chose salad.

How they use it: Use "percent of total" mode for each: 30 is what % of 50? (60%), 12 is what % of 50? (24%), etc.

Outcome: Clear presentation: "60% prefer pizza, 24% sandwiches, 16% salad" — much more impactful than raw numbers.

6. Calculating Tips and Splitting Bills

Situation: Dinner bill is $125, you want to leave an 18% tip.

How you use it: Calculate 18% of 125 = $22.50. Total with tip = $147.50. If splitting among 4 people, divide by 4 = $36.88 each.

Outcome: Fair tip calculation and equal split, all done in seconds.

7. Tracking Budget Changes

Situation: Your monthly grocery budget was $400, but recent prices pushed it to $460. You need to understand the impact.

How you use it: Use percent change: from 400 to 460 = +15% increase.

Outcome: Clear context for adjusting your budget or finding savings elsewhere.