In an illustrative example, you reduce the price of a 10 000 forint product by 20%. The new price is 8 000 forints. If you later increase this by 20%, you get 9 600 forints. The reason for the discrepancy is the base of the percentage calculation.
Always find the base value
For the decrease, you started from 10 000 forints. 20% of this is 2 000 forints. For the increase, the base is already 8 000 forints, of which 20% is 1 600 forints.
How much increase restores the original price?
The missing 2 000 forints are compared to the current 8 000 forints: 2 000 / 8 000 × 100 = 25%. Therefore, in this example, a 20% decrease is offset by a 25% increase.
The restoration formula works for other percentages too
Let c be the proportion of the decrease in decimal form: for 20%, c = 0.20. The new price is the original price × (1 − c), and the shortfall is the original price × c. The required increase is the quotient of the shortfall and the new price:
Restoration increase percentage = c / (1 − c) × 100.
| Previous decrease | Required increase from the reduced value |
|---|---|
| 10% | 11.11% |
| 20% | 25% |
| 40% | 66.67% |
| 60% | 150% |
The table rounds to two decimal places; for exact restoration, use the unrounded ratio. For example, if a 20% decrease is followed by an equal increase, the two multipliers are 0.8 × 1.2 = 0.96, so 96% of the original value remains. Generally, the product of an equal decrease and increase is 1 − c².
The formula is usable for such positive prices when 0 ≤ c < 1. After a hundred percent decrease, the price is zero; you cannot increase it to a positive value using percentage multiplication. In such cases, the restoration must be specified as a forint amount.
Which value do you want to restore?
A 25% increase returns the original 10 000 Ft. A different result is needed if the product basket you would buy with that amount has also become more expensive in the meantime. In a separate illustrative case, your money decreased from 10 000 to 8000 Ft, while the price of the compared, unchanged basket increased by 10%. To restore the previous purchasing power, you need 11 000 Ft.
The increase required from 8000 Ft is 11 000/8000 − 1 = 37.5%. If you only increase the amount by 25%, you get back 10 000 Ft, but at the new price level, its previous purchasing power is 10 000/1.10 ≈ 9090.91 Ft.
Generally, with a previous decrease of proportion c and a basket price increase of proportion i, the increase restoring the previous purchasing power is (1 + i)/(1 − c) − 1. Both proportions should refer to the same starting and ending periods. The 10% price increase here is our own assumption; the role of the price level used for real value is also discussed in the ECB wage and purchasing power analysis.
Multiple discounts in succession
If a 10 000 forint product first receives a 20% discount, then a further 10% discount, the price becomes 8 000, then 7 200 forints. The total saving is 2 800 forints, which is 28% of the original price.
When does the order of discounts matter?
The order of two percentage multipliers does not change the final result without intermediate rounding, provided eligibility conditions remain unchanged. If the price is rounded after each step, or if a discount only applies above a certain amount threshold, the actual price calculation follows additional rules. Therefore, in the offer, look for the base amount, the eligibility threshold and the point of rounding alongside the percentage. A fixed forint coupon also represents a different operation. The following hypothetical offer starts at 10 000 Ft and combines a 20% discount with a 1000 Ft coupon:
- First the 20%, then the coupon: 10 000 × 0.8 − 1000 = 7000 Ft.
- First the coupon, then the 20%: (10 000 − 1000) × 0.8 = 7200 Ft.
The 200 Ft difference is 20% of the coupon. Before purchasing, check the offer terms to see whether the percentage is applied to the amount before or after the coupon, and whether the two discounts can be used together. The calculator computes the specified operation; check the contractual terms of the promotion separately.
If you are planning the discount as a seller, the remaining forint amount after the final price also matters. The guide to margin and profit markup (in Hungarian) shows how much discount fits alongside your costs.
Which calculator should you use?
- To find a given percentage of an amount, open the percentage calculator.
- To compare old and new values, choose the percentage change calculator.
- For successive price discounts, use the discount calculator.
For calculating the rate of change, the original value in this example is positive. At a base value of zero, the percentage change is not interpretable with this formula.
Calculate the reverse operation separately
If you first increase the 8000 Ft price by 25%, it becomes 10 000 Ft. From here, a 20% decrease brings it back to 8000 Ft. Generally, after this positive increase rate, the restoring decrease is e / (1 + e). Therefore, it is worth keeping the successive forint values alongside the offer: from these, the percentage in the correct direction can be directly verified later.
Final knowledge test
Choose one answer for each question. Each correct answer earns 1 point; an incorrect answer, a skipped question or more than one selected answer earns 0 points. You can score 0–3 points in total. Read the solutions after answering.
Question 1: After a fifty percent decrease, how much increase returns the starting positive amount?
- A) 50%.
- B) 75%.
- C) 100%.
Question 2: A price receives a 30% discount, then a further 20% discount. Without intermediate rounding, what is the total discount?
- A) 50%.
- B) 44%.
- C) 6%.
Question 3: Why can the order of a fixed coupon and a percentage discount yield different results?
- A) The fixed coupon is the same percentage in every order.
- B) Two discounts must always be added together in percentage.
- C) The coupon can modify the base amount for the percentage.
Solutions and explanations
- 1. C. The same amount must be added to the remaining half: 0.5 / 0.5 = 1. If you chose otherwise, review this again: restoration from the reduced base.
- 2. B. The remaining proportion is 0.70 × 0.80 = 0.56, so the discount is 44%. If you chose otherwise, review this again: successive percentage multipliers.
- 3. C. The article's example of 10 000 Ft yields final results of 7000 and 7200 Ft in the two orders. If you chose otherwise, review this again: the order of a fixed coupon and a percentage discount.
What does your result mean?
- 0 points: start with the basic relationship: restoration from the reduced base. Work through the related example in the article.
- 1 point: return to the explanation of the two missed questions and write down the correct inputs.
- 2 points: check the reference base and conditions on the topic of the skipped or incorrect question, then recalculate.
- 3 points: you correctly applied the three relationships examined. Try it with your own data, and note the limitations of the section on the order of a fixed coupon and a percentage discount.
Translated and adapted from the Hungarian article: Hungarian original.