מחשבון אחוזים

איך להשתמש במחשבון זה

1. הזן X (percentage or number)
2. הזן Y (number)
3. לחץ על כפתור חשב
4. קרא את התוצאה המוצגת מתחת למחשבון

How to Calculate Percentages

A percentage represents a number as a fraction of 100. The word itself comes from the Latin per centum — "by the hundred." The three core percentage calculations you will encounter are:

• Find X% of Y: Multiply Y by X/100. Example: 25% of 80 = 80 × 0.25 = 20
• X is what % of Y: Divide X by Y, then multiply by 100. Example: 30 is what % of 120? → (30/120) × 100 = 25%
• Percentage change: ((New − Old) / |Old|) × 100. Example: price rises from $40 to $50 → (10/40) × 100 = 25% increase

A fourth common calculation is reverse percentage: if a discounted price is $85 after a 15% reduction, what was the original? Original = 85 / (1 − 0.15) = 85 / 0.85 = $100.

Quick Mental Math Tricks for Percentages

You do not always need a calculator. These shortcuts save time in everyday situations:

• 10% trick: Move the decimal one place left. 10% of $73 = $7.30
• 5% trick: Halve the 10% value. 5% of $73 = $3.65
• 15% tip: Add 10% + 5%. 15% of $60 = $6 + $3 = $9
• 20% shortcut: Divide by 5. 20% of $85 = $17
• 1% rule: Move the decimal two places left, then scale. 3% of $250 = $2.50 × 3 = $7.50

For percentage change, a useful mental check: if something increases by 50% and then decreases by 50%, you do NOT end up where you started — you end up at 75% of the original. (100 → 150 → 75). This asymmetry trips up many people.

Real-World Percentage Examples

Percentages appear in nearly every financial and everyday calculation:

Percentage in Finance and Investing

Finance is built on percentages. Understanding them precisely can save — or make — you thousands of dollars:

• APR vs APY: A 12% APR compounded monthly yields an APY of (1 + 0.12/12)^12 − 1 = 12.68%. Always compare APY for savings accounts.
• Compound growth: At 7% annual return, $10,000 grows to $19,672 in 10 years. The 7% return compounding creates nearly double the money compared to simple interest ($17,000).
• Inflation impact: At 3% annual inflation, $100 today has the purchasing power of $74 in 10 years. Always measure investment returns after inflation.
• Mortgage rate difference: On a $300,000 30-year mortgage, the difference between 6.5% and 7.0% is approximately $100 per month — or $36,000 over the life of the loan.

The concept of basis points (bps) is commonly used in finance: 1 basis point = 0.01%. A rate change from 5.00% to 5.25% is an increase of 25 basis points.

Percentage vs Percentage Points: A Common Confusion

One of the most frequent errors in interpreting data is confusing percentage change with percentage points:

If an interest rate rises from 4% to 6%, it has increased by 2 percentage points — but that is a 50% increase (since 2 is 50% of 4). These two statements describe the same event but sound very different. Politicians and media often exploit this ambiguity.

Another important distinction: percentage vs percentile. A percentage is a proportion out of 100. A percentile indicates where a value falls in a ranked distribution. Scoring 85% on a test and scoring in the 85th percentile are entirely different — the 85th percentile means you outperformed 85% of test-takers, regardless of the actual score.

Percentage Error and Scientific Accuracy

In science and engineering, percentage error measures how far a measured value is from the true (accepted) value:

% Error = |Measured − True| / |True| × 100

Example: You measure a 250 mL beaker and get 243 mL. % Error = |243 − 250| / 250 × 100 = 2.8%. This is an excellent result for most lab purposes.

Percentage accuracy is the complement: 100% − % Error. In manufacturing, a tolerance of ±1% is often considered acceptable for most components.

Related concept: margin of error in surveys. A poll reporting "52% support, ±3%" means the true value is likely between 49% and 55%, making the outcome statistically uncertain.

Frequently Asked Questions