Percentages, discounts, and percentage points
Choose the right denominator, calculate a final discounted price, and distinguish a change in a rate from its relative percentage change.
Translate the question before entering numbers
A percentage can be an amount, a comparison, or an adjustment. Asking for 15% of 200 gives an amount: 30. Asking what percentage 30 is of 200 gives a rate: 15%. The same numbers occupy different fields, so check the mode and its field labels before calculating.
For a sale price, use Decrease by a percentage. Enter the original price as the first value and the discount rate as the second. Percentage of a number gives the discount amount instead of the price you will pay. Tax, delivery, and other charges require separate treatment; the calculator does not infer them.
Mode: Percentage of a number
Percentage: 15 · Number: 200
Expected result:
30
15 ÷ 100 × 200 = 30Mode: Decrease by a percentage
Original value: 200 · Percentage: 20
Expected result:
160
200 × (1 − 20 ÷ 100) = 160Keep percentage points separate from relative change
Suppose a measured rate moves from 10% to 15%. Subtracting the rates gives five percentage points. Relative change compares that five-point difference with the original rate: 5 ÷ 10 × 100 = 50%. Neither answer replaces the other; they describe different aspects of the change.
Use Percentage change with the numerical rate values 10 and 15 to obtain 50%. State the original and new rates alongside it when reporting the result. A phrase such as ‘up five percent’ would leave readers unsure which comparison you mean.
Mode: Percentage change
Original value: 10 · New value: 15
Expected result:
50% relative increase
(15 − 10) ÷ 10 × 100 = 50%
The absolute difference between the rates is 5 percentage points.Check the baseline and undefined cases
The baseline determines the answer. Moving from 80 to 100 is a 25% increase; moving from 100 to 80 is a 20% decrease. Reversing the original and new values therefore does more than reverse a sign. The original value must be entered first.
A relative change from zero is undefined because the formula divides by the baseline. Report the absolute change instead of treating the error as 0% or 100%. For negative baselines, ADEMN divides by the baseline’s absolute value to align the sign with the direction of movement. This is an explicit tool convention; label it when comparing results with a system that uses a different convention.
Apply successive adjustments in order
Two successive 20% discounts on 200 produce 160, then 128. The combined discount is 36%, not 40%, because the second reduction applies to the reduced price. Load the discount example, calculate 160, then use 160 as the next original value.
To check the final price, compare it with the initial 200 using Percentage change: the answer is −36%. For business reporting, retain your unrounded amounts until the agreed currency-rounding step. The tool displays numerical results to 12 significant digits; a retailer’s line-by-line tax and currency rules may differ.
| Step | Calculation | Result |
|---|---|---|
| First reduction | 200 × 0.8 | 160 |
| Second reduction | 160 × 0.8 | 128 |
| Overall reduction | (128 − 200) ÷ 200 × 100 | −36% |