# Percentages with a visible calculation path

> Percentage, rate and base value on the tape, plus discount, cash discount and markup: every rate shows its amount and its base – examples you can adapt.

- Language: English
- This page as HTML: https://www.calctape.com/en/percentage-calculation
- Updated: 2026-09-12

Percent means “per hundred” – and the mistakes rarely happen in the arithmetic
but in the question what the rate refers to. On the tape the reference is
always visible: a percentage acts on the sum of the lines above it, and the
amount it produces stands right beside it.

## Discount and cash discount: two percentages, two bases

A device is listed at 1,899 €. The dealer grants a 15 % discount, and a 2 %
cash discount is agreed for payment within 14 days. The cash discount refers
to the already discounted price – two percentages in a row are not the same as
17 % at once. Change the rates and watch the amount payable move.

| | Betrag | Posten |
|---|---:|---|
| | | *Purchase: device with discount and cash discount* |
|  | 1,899.00 | List price |
| - | 15 % (−284.85) | Dealer discount |
| = | **1,614.15** | Net price after discount |
| - | 2 % (−32.28) | Cash discount if paid within 14 days |
| = | **1,581.87** | Amount payable |

## Price increase and discount: 20 % up, 20 % back

A retailer raises the price of a device by 20 % and advertises a 20 %
discount a few weeks later. Afterwards the device costs less than before the
increase: the increase is taken from the old price, the discount from the
raised one. On the tape both amounts stand one below the other. Enter 25 % for
the increase, and a 20 % discount leads exactly back to the old price.

| | Betrag | Posten |
|---|---:|---|
| | | *Price increase, then discount* |
|  | 749.90 | Price before the increase |
| + | 20 % (149.98) | Price increase |
| = | **899.88** | Price after the increase |
| - | 20 % (−179.98) | Sale discount |
| = | **719.90** | Sale price |

## The three basic tasks

Percentage, rate, base value: on the tape each of them is a short calculation.
`* 15 %` takes the share of a number, a division by the base value and `* 100`
turn an amount back into a rate, and `/ 119 %` works from the whole back to the
base value. Behind `*` and `/` CalcTape writes the factor it used.

| | Betrag | Posten |
|---|---:|---|
| | | *Percentage: 15 % of 1,899* |
|  | 1,899.00 | List price |
| × | 15 % | share of it |
| = | **284.85** | Discount amount |
| | | |
| | | *Rate: what share is 317.13?* |
|  | 317.13 | Reduction |
| ÷ | 1,899.00 | List price |
| × | 100.00 | in percent |
| = | **16.70** | Reduction in percent |
| | | |
| | | *Base value: 238 is 119 %* |
|  | 238.00 | Amount with the markup |
| ÷ | 119 % | of the base value |
| = | **200.00** | Base value |

## What the calculation shows

- **The reference is the sum above.** Every percentage line works with the
  running total – the cash discount with the discounted price, not with the
  list price. That is exactly how discount, tax and cash discount build on
  each other.
- **The amount sits beside the rate.** 15 % sounds abstract, 284.85 € is an
  amount you can place. CalcTape writes it there automatically.
- **Percent of percent becomes visible.** 15 % and 2 % in a row are 16.7 % off,
  not 17 %; and a 20 % increase followed by a 20 % discount ends at 719.90
  instead of 749.90. The tape shows the reason in the line in between: 149.98
  are added, 179.98 come off.
- **Change the order, let it recalculate.** Swap lines or change a rate – every
  result below recalculates at once. If VAT came into it, it would sit between
  discount and cash discount – see [calculating VAT](https://www.calctape.com/en/vat-calculation).

## How to do it in CalcTape

1. The first line is the base value: `1899 List price`.
2. Write percentages with operator and percent sign: `- 15%` subtracts,
   `+ 20%` adds – based on the sum above, see
   [percentage calculations](https://www.calctape.com/en/manual-web#percentage-calculations) in the manual.
3. The `=` key (or Enter) keeps an interim result; the calculation continues
   below it. For discount rates you need often, a key of your own is worth
   setting up – see
   [customizing user keys](https://www.calctape.com/en/manual-web#5-customizing-user-keys-vat).

## Related calculations

Percent on percent is also at work in the [quote](https://www.calctape.com/en/quote-calculation) –
tax on the subtotal, cash discount on the gross amount – and in
[VAT](https://www.calctape.com/en/vat-calculation), there with the way back from gross to net.