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20% off $30 is $24

A 20% discount means you pay 80% of the price: $30 × 0.8 = $24, saving $6.

Percent of, off, change Worked answer, not just a number Nothing leaves your browser
15% of 200
30
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What is 20% off $30?

  • You pay: $24
  • You save: $6
  • Working: $30 × 80⁄100 = $24

The four percentage calculations, and when each one applies

Every percentage question you will ever meet is one of four shapes. Naming the shape first is what stops the classic mistakes.

N × P⁄100

P% of N. Tips, commission, deposits, interest. 15% of $200 → $30.

N × (100−P)⁄100

P% off N. Sales and discounts — compute what you pay, not what you save. 30% off $80 → $56.

A ÷ B × 100

A is what % of B. Test scores, market share, progress. 42 of 60 → 70%.

(new−old) ÷ old × 100

% change. Price rises, growth, drops. 80 → 100 is +25%; 100 → 80 is −20%.

The base is everything

Nearly every percentage error is a wrong base — dividing by the new value instead of the old one, or taking a percentage of the discounted price instead of the original. The rule that fixes all of them: the base is the number the percentage is "of", which in change problems is always the value you started from.

It is also why percentages do not add. A 20% rise followed by another 20% rise is not 40% — it is 44%, because the second rise acts on a bigger base (1.2 × 1.2 = 1.44). Compounding is just this effect repeated.

Mental shortcuts that survive real life

  • 10% is one decimal shift. 10% of $87.50 is $8.75. Nearly everything builds from this: 5% is half of it, 20% is double, 15% is one-and-a-half.
  • x% of y equals y% of x. 8% of 25 feels hard; 25% of 8 is obviously 2. Same number.
  • For discounts, think "what fraction do I pay". 25% off means you pay ¾. A $59.99 jacket at 25% off is about $45 before you reach for a phone.

Doing money maths? These go further

Percentages with dollar signs attached usually mean GST, margin or pricing — each has its own tool with the right defaults built in.

GST calculator

15% has one special case in New Zealand: finding the GST already inside a price is ÷23×3, not ×0.15. This tool does both directions correctly.

gst.amit.marketing →

Markup & margin

A 25% markup is not a 25% margin — confusing them quietly shrinks profit. Work out sell price from either.

markup.amit.marketing →

Pay converter

Salary to hourly and back, including what a percentage pay rise actually means per week.

pay.amit.marketing →

Percentage questions, answered

How do I work out a percentage of a number?
Turn the percentage into a decimal by dividing it by 100, then multiply. So 15% of 200 is 0.15 × 200 = 30. The reverse works too: multiplying by 1.15 adds 15% on top, which is why that shortcut appears everywhere from tipping to GST.
How do I take a percentage off a price?
Multiply the price by (100 minus the discount) divided by 100. A 30% discount means you pay 70% of the sticker price: $80 × 0.70 = $56. Working out what you pay directly is quicker and less error-prone than working out the saving and subtracting it.
How do I work out what percent one number is of another?
Divide the part by the whole and multiply by 100. Scoring 42 out of 60 is 42 ÷ 60 × 100 = 70%. The order matters — the number after 'of' is always the one you divide by.
How is percentage change calculated?
Take the change (new minus old), divide it by the original value, and multiply by 100. Going from 80 to 100 is a 25% increase (20 ÷ 80), but going from 100 back to 80 is only a 20% decrease (20 ÷ 100). The asymmetry trips people up constantly — the base is always the number you started from.
Why is a 50% increase not cancelled by a 50% decrease?
Because the base changes. Increase 100 by 50% and you have 150; decrease 150 by 50% and you are at 75, not 100. Successive percentages multiply rather than add — a 20% rise followed by a 20% fall leaves you at 96% of where you began.
What is a percentage point?
The absolute difference between two percentages. If interest rates go from 4% to 6%, that is a rise of 2 percentage points — but a 50% increase in the rate itself. News reports mix these up routinely, and the difference is enormous.
Does the calculator store what I type?
Only in your own browser, so your last calculation is still there when you come back. Nothing you enter is sent to a server.

Common calculations

Straight to the answer for the pairs people look up most.

Percent of a number

10% of 10015% of 20020% of 15025% of 20010% of 50015% of 1,00020% of 50030% of 3005% of 2,00015% of 5,00025% of 1,00030% of 1,500

Percent off a price

20% off $5030% off $8025% off $10040% off $6050% off $12010% off $15015% off $20070% off $10030% off $15020% off $2560% off $8075% off $40

Pairs well with the percentage calculator

GST calculator Add or remove 15% GST instantly add or remove 15% GST → Markup calculator Margin, markup and the right sell price work out margin and markup → Day counter Days between dates, countdowns, NZ holidays count days between dates →

The rest of the toolkit

Twelve free tools that talk to each other — send hours or an accepted quote straight into an invoice without retyping a thing. No signup on any of them.

Invoice generator Compliant GST tax invoice, PDF in one click make a GST tax invoice → Quote generator Win the job, then convert it to an invoice send a professional quote → Receipt maker Proof of payment with the GST split out issue a payment receipt → Hours calculator Timesheets, breaks, billable hours add up hours worked → Rate calculator What you must charge per hour set your hourly rate → Pay converter Salary to hourly, both directions convert salary to hourly → Mileage calculator IRD kilometre-rate claims done right claim vehicle mileage → Sleep calculator The bedtime that beats the 6am alarm find your best bedtime →