Calculator Wizard

1. Basic Percentage Formula

Formula: (Part ÷ Whole) × 100

Use this whenever you know a part and a whole, and want to express the part as a percentage. It's the foundation every other formula on this page builds from.

Example: You got 15 out of 60 questions correct. (15 ÷ 60) × 100 = 25%.

2. Percent of a Number

Formula: (X ÷ 100) × Y

Use this to find what a given percentage of a number actually equals — like figuring out a discount or a tax amount before you add it in.

Example: 20% of a $50 bill. (20 ÷ 100) × 50 = $10.

3. What Percent Is X of Y?

Formula: (X ÷ Y) × 100

Use this when you have two numbers and want to know what percentage the first represents of the second — the reverse of the formula above.

Example: 12 is what percent of 40? (12 ÷ 40) × 100 = 30%.

4. Percentage Increase or Decrease

Formula: ((New − Old) ÷ Old) × 100

Use this to measure how much a value has grown or shrunk relative to its starting point — always divide by the original value, never the new one.

Example: Price rises from $40 to $50. ((50 − 40) ÷ 40) × 100 = 25% increase.

5. Tip Calculation Formula

Formula: (Tip % ÷ 100) × Bill

Use this to calculate a tip amount from a percentage and a bill total — the same structure as "percent of a number," applied to a restaurant check.

Example: 18% tip on a $60 bill. (18 ÷ 100) × 60 = $10.80.

1. Forgetting to Convert Percent to Decimal

25% = 0.25, not 25. Plugging the raw number 25 straight into a formula instead of 0.25 gives an answer 100 times too large.

Fix: Always divide the percent by 100 before multiplying — every formula on this page does this as its first step.

2. Dividing the Wrong Way

To find what percent X is of Y, divide X by Y — not Y by X. Flipping the division gives a completely different, usually much larger, number.

Fix: Correct formula is (Part ÷ Whole) × 100. The "part" always goes on top.

3. Mixing Up Increase and Decrease

Always divide by the original (starting) value, not the new one. Using the wrong base value silently changes the answer, especially on large swings.

Example: 40 → 50 is a 25% increase, but 50 → 40 is a 20% decrease — not the same percentage in reverse.

4. Adding Percentages Incorrectly

Stacked percentages don't simply add together. "25% off, then an extra 10% off" is not 35% off in total.

Example: $100 × 0.75 × 0.90 = $67.50 — a real discount of 32.5%, not 35%, since the second discount applies to the already-reduced price.

5. Forgetting That Percentages Are Relative

A jump from 10 to 20 is a 100% increase, not 10 — percentage change depends entirely on the starting value.

Example: Going from 10 to 20 doubles the value, which is a 100% increase, even though the raw difference is only 10.