Percentage calculator

Here are the situations Americans run into most often, solved with the same four calculations this tool performs:

• Tipping at a restaurant: an 18% tip on a $64 dinner bill is 18 / 100 × 64 = $11.52, so you'd leave $75.52 total.
• Sale price: a $129.99 jacket at 25% off costs 129.99 × (1 − 25/100) = $97.49, saving you $32.50.
• Pay raise: a 4% raise on a $52,000 salary takes you to 52,000 × (1 + 4/100) = $54,080 a year.
• What percent of income goes to rent: if you earn $4,200 a month and pay $1,470 in rent, that's 1,470 / 4,200 × 100 = 35% of your income.
• Sales tax estimate: 8.875% tax on a $250 purchase in New York City adds 8.875 / 100 × 250 = $22.19.

In every case you only need two numbers: the percentage (X) and the base amount (Y). The calculator returns all four results at once — the percentage of the amount, the inverse percentage, the increased value, and the decreased value — so you never have to figure out which formula fits your problem; the right answer is always among the four.

You only need to fill in two fields:

1. Percentage (X): the percent you want to work with. Decimals are fine (for example, 8.875 for NYC sales tax or 3.5 for a raise), and negative values work too if you want to model a drop. 2. Amount (Y): the base amount the percentage applies to, such as a price tag, a bill, or your monthly salary.

Four results appear instantly:

• X% of Y: the value of the percentage. Use this to find a discount amount, a tip, or the tax on a purchase.
• X as a % of Y: treats X as a plain amount and tells you what percent it represents of Y. Handy for figuring out what share of your budget an expense takes.
• Y increased by X%: the amount after adding the percentage, like a price with tax or a salary after a raise.
• Y decreased by X%: the amount after subtracting the percentage, like a sale price after a markdown.

There is no button to press: the results recalculate automatically every time you change a value, so you can compare several scenarios in seconds.

All four operations in this calculator rest on very simple formulas. In plain text:

• X% of Y = (X / 100) × Y
• X as a percentage of Y = (X / Y) × 100
• Y increased by X% = Y × (1 + X / 100)
• Y decreased by X% = Y × (1 − X / 100)

Worked example, step by step. Your dinner bill is $64 (Y = 64) and you want to tip 18% (X = 18):

1. Tip amount: (18 / 100) × 64 = 0.18 × 64 = $11.52. 2. Inverse percentage: (18 / 64) × 100 = 28.13% (that's what the number 18 represents out of 64). 3. Increased value: 64 × (1 + 18/100) = 64 × 1.18 = $75.52, the total you'd hand the server. 4. Decreased value: 64 × (1 − 18/100) = 64 × 0.82 = $52.48 (what the bill would be after an 18% discount instead).

A handy mental shortcut: 10% of any amount is just the number with the decimal point moved one place left (10% of $64 is $6.40), so 18% is roughly $6.40 × 2 minus a fifth of $6.40. The calculator does the exact version of this math to two decimal places.