What's the difference between percent and percentage points?

A rate going from 40% to 35% fell 5 percentage points, which is a 12.5% fall in the rate itself. 4.00% to 4.25% is up 0.25 points, also called 25 basis points, or 6.25%.

How is percent change worked out from a negative start?

The change is divided by the size of the start, ignoring its sign: −200 to 100 is a change of +300 on a base of 200, so +150%. Dividing by −200 would report −150% for a number that rose. From a start of 0 there's no base, so the calculator gives the change itself instead of a percent.

Why doesn't a 50% gain undo a 50% loss?

The gain is measured on a smaller base. 100 falls 50% to 50; 50% of 50 is 25, so you're at 75. Getting back to 100 takes +100%.

Where does the stock price come from?

You type your start price. The latest close can be typed, or loaded as a ticker's latest official end-of-day close. It's price change only: dividends aren't included.

ALGOTHESIS / RESEARCH TOOLS

Percentage calculator

Up 50%, down 50%, and somehow not even.

Parts of a whole

What is%of?

200 × 15 ÷ 100 = 30

is what percent of?

30 ÷ 200 × 100 = 15%

Change

Fromtois a change of

(80 − 64) ÷ |64| × 100 = +25%The start goes in as its size, so −200 → 100 is +150%.

up and down by%

500 × 1.10 = 550 · 500 × 0.90 = 450

after a%change was

44 ÷ (1 − 0.10) = 48.89Not 48.4: adding 10% of 44 uses the wrong base.

Comparing

The difference betweenand

|5 − 6| ÷ ((5 + 6) ÷ 2) × 100 = 18.18%Same either way round; refused if one is below 0 and the other above.

A rate from%to%

35 − 40 = −5 points · −5 ÷ 40 = −12.5%4.00% → 4.25% is +25 bps, or +6.25%.

Losses

After a fall of%it takes this to get back

1 ÷ (1 − 0.50) − 1 = +100%−75% needs +300%; −90% needs +900%.

Stock price change

Your start price against a stock's latest official close.

Example · prices typed

Latest close

Start price

Start price (typed): $95.00
Latest close (typed): $89.79
Change per share: −$5.21
On 100 shares: −$521.00
Back to $95.00 needs: +5.80%
Price change: −5.48%

Closes only, price change only, dividends not included.

How far back is even?

Yours now

−5.48%

+5.80%

−10%

−10%

+11.1%

−20%

−20%

+25%

−25%

−25%

+33.3%

−33.3%

−33.3%

+50%

−50%

−50%

+100%

Each pair: a fall, then the rise that undoes it, on one scale. The rise is always bigger, because it starts from the lower price.

How percentages work

A percent is a share of 100, so every question here is one multiplication or one division. What changes from question to question is the base: the number you measure against.

Most mistakes come from the base. A rise is measured from where you started, a fall from where you were, and a reverse calculation from the number before the change. That's why +25% and −20% describe the same pair of numbers, and why +50% doesn't undo −50%.

The stock section is the same arithmetic on prices: your start price, the latest official close, and the rise it would take to get back.

Questions

What's the difference between percent and percentage points?: A rate going from 40% to 35% fell 5 percentage points, which is a 12.5% fall in the rate itself. 4.00% to 4.25% is up 0.25 points, also called 25 basis points, or 6.25%.
How is percent change worked out from a negative start?: The change is divided by the size of the start, ignoring its sign: −200 to 100 is a change of +300 on a base of 200, so +150%. Dividing by −200 would report −150% for a number that rose. From a start of 0 there's no base, so the calculator gives the change itself instead of a percent.
Why doesn't a 50% gain undo a 50% loss?: The gain is measured on a smaller base. 100 falls 50% to 50; 50% of 50 is 25, so you're at 75. Getting back to 100 takes +100%.
Where does the stock price come from?: You type your start price. The latest close can be typed, or loaded as a ticker's latest official end-of-day close. It's price change only: dividends aren't included.

Educational only, not investment advice or a recommendation to buy or sell anything. The stock section uses official end-of-day closes. AlgoThesis is a publisher, not an adviser; see the disclaimer.Prices: Data provided by Databento (end of day)