Percentage Calculator

Two headlines can describe the exact same event and sound completely different: "Interest rate rises 2 percentage points" versus "Interest rate jumps 40%." Both are accurate. They're just measuring two different things, and mixing them up is one of the most common — and most consequential — everyday math mistakes.

The Core Distinction

Worked Example: An Interest Rate Increase

Suppose a savings account's interest rate rises from 5% to 7%.

• In percentage points: 7 − 5 = 2 percentage points
• In percentage change: (7 − 5) ÷ 5 × 100 = 2 ÷ 5 × 100 = 40%

Both descriptions are correct. "Rose 2 percentage points" and "rose 40%" describe the identical change — but they land very differently. A 2-point move sounds incremental; a 40% jump sounds dramatic. Neither framing is dishonest on its own, but conflating the two — quoting the percentage-change figure while letting a reader assume it means percentage points, or vice versa — is where real confusion sets in.

Worked Example: A Tax Rate Cut

A state cuts its sales tax rate from 25% to 20%.

• In percentage points: 25 − 20 = 5 percentage point cut
• In percentage change: (20 − 25) ÷ 25 × 100 = −5 ÷ 25 × 100 = −20% (a 20% reduction)

Again, both are true simultaneously. A "5-point cut" and a "20% cut" refer to the same policy change.

The Formula for Percentage Change

The key detail people miss: the denominator is always the original value, not the new one — and not the difference between them.

Why This Matters More at Low Base Values

The gap between the two measures grows larger the smaller the starting percentage is. A move from 1% to 3% is only "2 percentage points" but represents a 200% relative increase — triple the original rate. This is why percentage-point framing is often used for small base rates (it sounds calmer) while percentage-change framing is used for the same data when a more dramatic-sounding figure is wanted. Neither is inherently more "correct" — but knowing which one you're reading changes how you should interpret the news.

How to Read Financial and Economic Headlines Carefully

• If a headline uses the exact phrase "percentage points", it's describing simple subtraction between two rates.
• If it just says "percent" or "%" attached to a change (e.g., "rose by 40%"), it's almost always describing relative percentage change — which requires knowing the original base value to interpret correctly.
• Central bank rate decisions, inflation reports, and unemployment figures are the areas where this distinction shows up most often — and where misreading it most commonly leads to overreacting (or underreacting) to news.

A Related Everyday Case: Stacked Discounts

The same "subtract vs. relative" confusion shows up in retail discounts — a 25%-off sale combined with an extra 10%-off coupon does not equal 35% off, because the second discount applies to the already-reduced price, not the original one. The math is different from the percentage-points issue above, but the underlying lesson is the same: percentages don't simply add together across different bases.