Percentage Calculator

How do you calculate a percentage?

A percentage is a share out of a hundred, so every calculation is one of two moves: divide to find a share, or multiply to apply one.

• Percent of a number: multiply and divide by 100. Fifteen percent of 80 is 80 x 15 / 100, which is 12.
• Share of a total: divide and multiply by 100. Twelve out of 80 is 12 / 80 x 100, which is 15 percent.
• Percent change: the difference divided by where it started. From 80 to 92 is 12 / 80, a 15 percent increase.

In your head, ten percent is the decimal point moved one place. Everything else is built from that: five percent is half of it, twenty is double, fifteen is one plus a half.

The percentages that turn up on an invoice

Every one of these is the same arithmetic wearing a different hat. The presets above load them, so you can check a real figure rather than a textbook one.

• Deposit. Twenty-five to fifty percent before work starts. On a $7,668 job, a 30 percent deposit is $2,300.40 and leaves $5,367.60 on completion. Put both figures on the quote so nobody is converting in their head later.
• Retention. Commonly five percent held back until sign-off. Show it as its own line with the release date: it is money you have earned and are waiting on.
• Card and platform fees. Around 2.9 percent plus a fixed charge. On $7,668 that is $222.37, and it comes out of margin rather than revenue, so on a twenty percent margin it is closer to fifteen percent of the profit on that job.
• Tax inside a total. A $7,668 gross figure at twenty percent contains $1,278 of tax, not $1,533.60. The VAT calculator works this both ways.
• Discounts. Twenty percent off then a further ten is twenty-eight percent, not thirty. The discount calculator handles stacking and shows what it costs your margin.
• Late payment. A stated percentage per month, or an early settlement discount worth far more than it looks. The late fee calculator covers both.
• Price changes. A supplier's percentage increase, or a percentage decrease you pass on. Percentage change is measured against where the figure started, not against where it ended, which is why a rise and a fall of the same percentage do not cancel out.

Once the percentages are settled, the invoice generator puts them on the document as their own lines, which is what stops a client querying the total.

Markup, margin and the percentage that is not what you think

Two figures describe the same profit and they are never equal. Markup divides profit by cost; margin divides it by price. A thirty percent markup leaves a 23.1 percent margin, and quoting one while meaning the other is the most expensive percentage error in small business.

The markup calculator converts between them from the cost side, and the profit margin calculator from the price side.

Reversing a percentage is division, not subtraction

This is the one that costs money. If a price is $120 after a 20 percent increase, the price before was not $96. It was $100, because $120 is 120 percent of what you are looking for: $120 divided by 1.20.

The same arithmetic removes tax from a gross figure, works a net price back out of a marked up one, and finds the list price behind a discount. If you are working with sales tax or VAT specifically, the sales tax calculator does it both ways.

Percent against percentage points

A rate that moves from 5 percent to 7 percent has risen two percentage points, and it has risen 40 percent. Both statements are true, and they sound wildly different, which is exactly why press releases pick one and complaints pick the other.

• Points are the plain difference between two rates. Use them for interest rates, tax rates, conversion rates and margins.
• Percent is that difference relative to where it started. Use it when the size of the move matters more than the level.

When somebody quotes you a big-sounding percentage, ask which of the two they mean.

Changes do not cancel out

Down 20 percent then up 20 percent leaves you at 96, not 100, because the second change is calculated from a smaller number. The bigger the swing, the worse it gets: a 50 percent fall needs a 100 percent rise to recover, and an 80 percent fall needs 400 percent.

This is why a discount cycle is expensive, why a bad quarter takes more than one good quarter to undo, and why stacked discounts are always smaller than they sound. The discount calculator handles the stacked case directly.

Where percentages catch people out, trade by trade

• Trades and contractors: a 10 percent waste allowance on materials is 10 percent of the quantity, not 10 percent added to the price after markup. Apply it before you price.
• Retail: margin and markup are both percentages of different things. A 50 percent markup is a 33.3 percent margin, and the markup calculator converts between them.
• Freelancers: a 30 percent tax set-aside comes off profit, not turnover, or you will over-save all year and under-price all year.
• Hospitality: a 20 percent tip on the post-tax total is not a 20 percent tip on the bill. On a large check the gap is real money.
• Employed: a five percent raise is not five percent more in your account, because tax and payroll deductions take their share of the increase too.
• Anyone quoting: adding 20 percent to cover a 20 percent fee leaves you short. To keep a fee whole, divide by 0.80 rather than multiplying by 1.20.