Percentage Calculator

To calculate a percentage of a number, multiply the number by the percentage and divide by 100. For example, 20% of $350 = $350 * 20 / 100 = $70. In New Zealand, this calculation comes up constantly: KiwiSaver contributions at 3% of gross salary, ACC levies at approximately 1.75% of liable earnings, and GST at 15% of ex-GST prices. A quick shortcut is to move the decimal point — 10% of any number is just the number divided by 10, and you can scale up or down from there (e.g. 5% is half of 10%, 15% is 10% + 5%). Most smartphone calculators support a direct percentage key. For financial planning in NZ, understanding percentages is essential for comparing interest rates, KiwiSaver fund growth, and mortgage repayments. Source: General mathematics.

To calculate a percentage change between two values, subtract the original from the new value, divide by the original value, and multiply by 100. Formula: ((New - Old) / Old) * 100. A positive result is an increase; a negative result is a decrease. For example, if your rent rises from $480 to $530 per week: (($530 - $480) / $480) * 100 = 10.4% increase. In New Zealand this is useful for tracking annual pay rises against inflation (the CPI), comparing property sale prices to purchase prices to assess capital gain, and monitoring mortgage interest rate changes. For the reverse — finding a new value after a known percentage change — multiply the original by (1 + rate/100) for an increase, or (1 - rate/100) for a decrease. Source: General mathematics.

A percentage is a proportion expressed out of 100, while a percentage point is the arithmetic difference between two percentages. This distinction matters enormously in finance. For example, if a mortgage interest rate rises from 6% to 7%, that is a rise of 1 percentage point — but it is also a 16.7% increase in the rate itself ((7-6)/6 * 100). In NZ financial reporting, the Reserve Bank often discusses OCR changes in percentage points (e.g., a 25 basis point rise equals 0.25 percentage points). KiwiSaver contribution rate changes — say from 3% to 4% employee contribution — are 1 percentage point changes. Confusing the two can lead to significant misunderstanding; a fund that grows from 5% to 6% return has improved by 1 percentage point, but by 20% in relative terms. Source: General mathematics and RBNZ communications.

Reverse percentage calculation finds the original value before a percentage was applied. If you know the final value and the percentage that was added or removed, divide the final value by (1 + rate/100) for an addition, or by (1 - rate/100) for a subtraction. The most common NZ example is removing GST: a GST-inclusive price of $230 was reached by adding 15%, so the ex-GST price is $230 / 1.15 = $200. Another example: a property sold for $650,000 after a 12% capital gain — the original purchase price was $650,000 / 1.12 = $580,357. This technique is also used to find a pre-discount price: if a sale item is $85 after a 15% discount, the original price was $85 / 0.85 = $100. Source: General mathematics.