Algebra Calculator

To find a percentage manually, convert the percentage to a decimal and multiply. For 18% of 250, change 18% to 0.18, then multiply: 0.18 × 250 = 45. For a quick mental estimate, find 10% by moving the decimal one place left (25), then take half of that for 5% (12.5), and add for 15% (37.5). Adjust for the remaining 3% by finding 1% (2.5) and multiplying by 3 (7.5), then adding to 37.5 to get 45. This method works for any percentage, but the Algebra Calculator does it instantly and avoids arithmetic errors. If you need to compare two percentage changes, use the percentage-change-calculator to see the relative difference.

Percentage refers to a portion of a whole, like 20% of 500 = 100. Percent change measures how much a value has increased or decreased relative to its original amount. For example, if a stock goes from $40 to $50, that's a 25% increase: (50 − 40) ÷ 40 = 0.25. If it then drops from $50 to $45, that's a 10% decrease: (50 − 45) ÷ 50 = 0.10. Notice the base changes each time. The Algebra Calculator handles both types when you select the right operation. For dedicated percent change calculations, the percentage-change-calculator gives you the exact percentage difference between two numbers.

To add a percentage, multiply the number by (1 + percentage as decimal). For a 15% raise on a $60,000 salary: 60,000 × 1.15 = $69,000. To subtract, multiply by (1 − percentage as decimal). For a 25% discount on a $120 item: 120 × 0.75 = $90. You can also calculate the percentage amount first and then add or subtract: 15% of 60,000 is 9,000, so 60,000 + 9,000 = 69,000. The Algebra Calculator automates this. If you're working with multiple increases, like a 5% raise followed by a 3% bonus, use the percentage-increase-calculator to see the combined effect, which is 8.15%, not 8%.

A reverse percentage finds the original number when you know a percentage of it. If a $45 shirt is 30% off and you paid $31.50, you can find the original price: $31.50 ÷ 0.70 = $45. This is useful for finding pre-tax prices, original salaries before a raise, or a population before a decline. For example, if a town's population is 8,500 after a 15% increase, the original was 8,500 ÷ 1.15 ≈ 7,391. The Algebra Calculator can perform this if you input the final value and percentage, then interpret the result as the original. For more complex reverse calculations, the percentage-calculator offers a dedicated reverse mode.

For a tip, multiply the bill by the tip percentage as a decimal. A 20% tip on a $75 bill: 75 × 0.20 = $15, total $90. For sales tax, add the tax rate to 1 and multiply. A 7% tax on a $200 purchase: 200 × 1.07 = $214. If you want to combine a tip and tax, apply them separately or multiply by (1 + tax rate + tip rate). For a $50 meal with 8% tax and 18% tip: 50 × (1 + 0.08 + 0.18) = 50 × 1.26 = $63. The Algebra Calculator handles each step. For mortgage-related percentage calculations, like down payments or interest, the mortgage-calculator provides specialized tools.

Because the second percentage applies to a different base. Start with 100. A 10% increase gives 110. Then a 10% decrease on 110 gives 99, not 100. The decrease is calculated on the larger number, so it removes more value. The net change is a 1% loss: (99 − 100) ÷ 100 = −0.01. This is why investment losses require larger gains to recover: a 20% drop needs a 25% gain to break even. For example, $1,000 losing 20% becomes $800; to get back to $1,000, it needs a 25% increase ($800 × 1.25 = $1,000). The Algebra Calculator shows each step, and the percentage-change-calculator helps you see the net effect of multiple changes.