Is tax applied before or after the discount?

After. In most jurisdictions, sales tax is calculated on the discounted price, not the original. So if a $100 item is 20% off and tax is 8%, you pay tax on $80 (the discounted price), not $100. Our calculator follows this convention.

How do I calculate percentage change?

Percentage change = ((new − old) / |old|) × 100. A positive result means an increase; a negative result means a decrease. Example: from 100 to 120 gives ((120 − 100) / 100) × 100 = 20% increase.

Why is percentage change undefined when the original value is zero?

Dividing by zero is mathematically undefined. Conceptually, any change from zero is infinite — going from 0 to 10 is 'infinitely' more, which isn't meaningful as a percentage. The tool explains this in the result card.

Can I use negative numbers?

Yes. Negative original values work in the change mode — the formula uses the absolute value of the original in the denominator so the sign reflects the direction of change. Negative percentages and negative prices will produce mathematically correct (but sometimes surprising) results.

How many decimals are shown?

Results are rounded to 4 decimals internally and displayed with up to 2 decimals. Currency values use 2 decimals with proper formatting. This is precise enough for everyday use — prices, discounts, and typical percentage calculations.

Does the discount calculator compound discounts?

No — it applies a single discount percentage. For a stacked discount (e.g., 20% off then 15% off), enter the combined effective discount, or calculate the two steps separately. Compounded discounts multiply: 0.8 × 0.85 = 0.68, so 20% + 15% = 32% effective discount, not 35%.

Is this calculator accurate for financial use?

The math is exact within floating-point precision (~15 significant digits). Results are displayed rounded for readability. For formal financial documents, verify against your accounting software — but for everyday retail, budget, and planning purposes, the calculator is accurate.

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3 Modes · Step-by-Step · Instant

Percentage & Discount Calculator

Three percentage calculators in one: find what X% of Y is, calculate a discounted price with optional sales tax, or measure the percentage change between two values. Every result includes a step-by-step formula breakdown so you can see exactly how it's computed.

#Percent of#Discount#Change#Tax#Step-by-step#Free

What is X% of Y?

Percentage

Value

15% of 200 is30

15% × 200

Steps

1Convert percent to decimal: 15% = 0.15

2Multiply: 0.15 × 200 = 30

Remainder

170

Remainder percent

85%

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How to use the percentage calculator

Three tools in one — pick the mode that matches your need.

X% of Y — quick percent of

Use this mode to find what a percentage of a value is. Example: what is 15% of 200? Enter 15 in the percentage field and 200 in the value field. The result and formula update instantly.

Discount — sale prices with optional tax

Enter the original price and the discount percent to see the savings, the discounted price, and the final price. Toggle 'Add sales tax' to layer tax on top of the discounted price — the order matters (tax applies after discount).

Change — percentage increase or decrease

Enter the original value and the new value to see the percentage change, along with the difference, multiplier, and direction (increase or decrease). If the original value is zero, the change is undefined — the tool explains why.

Frequently Asked Questions

Multiply the percentage (as a decimal) by the value. For example, 15% of 200 = 0.15 × 200 = 30. The formula step is shown in the result card.

About the Percentage & Discount Calculator

Everything you need to know

The three percentage questions that come up most often

In everyday life, percentage math falls into three categories. First, 'What is X% of Y?' — used for tips, tax calculations, and quick mental math. Second, 'What's the final price after a discount?' — used for shopping, retail, and business pricing. Third, 'How much did this change by?' — used for growth, inflation, performance, and any comparison of two values over time. This calculator handles all three with a single interface and step-by-step formula breakdowns.

Understanding percentage change vs. percentage points

A common confusion: percentage change and percentage points are different things. If unemployment goes from 5% to 6%, that's a 1 percentage point increase, but a 20% increase in relative terms. Our change calculator measures percentage change (the relative increase), which is the more common interpretation. When someone says 'unemployment rose 20%,' they mean percentage change. When they say 'rose 1 percentage point,' they mean absolute difference in percentage terms — which is just subtraction.

How discounts and tax interact

Retail math has a specific order of operations: discount first, then tax. This isn't arbitrary — it's how tax authorities in most jurisdictions require it. If you buy a $100 item with 20% off and 8% sales tax, you pay $80 × 1.08 = $86.40. The effective savings versus the un-discounted price is $13.60, not $20, because the tax calculation reduces the absolute savings. The tool shows this effective savings so you know exactly what you saved versus paying full price plus tax.

Why the formula breakdown matters

Knowing the answer is useful; knowing how it was computed is powerful. Each result card shows the exact intermediate steps — decimal conversion, multiplication, subtraction, and final rounding. This turns the calculator into a learning tool: students can verify their own mental math, shoppers can double-check a store's discount, and business owners can audit pricing calculations before they go live. The step-by-step explanation is also unique to each mode — the discount mode shows the tax step only when tax is enabled, and the change mode explains the divide-by-zero case when the original value is zero.