Percentage calculations come up every day: the sale discount in a shop window, the VAT on an invoice, the interest portion of a loan. But which formula applies when? Our calculator solves all three basic types of percentage problem – and shows the working so you can follow along.
Step by Step: How to Use the Percentage Calculator
- Choose the problem type: Calculate the percentage amount (W = ?), find the percentage rate (p = ?) or find the base value (G = ?).
- Enter the known values: e.g. for the percentage amount: base value G = €250, percentage p = 15%.
- Calculate: W = G × p/100 = 250 × 15/100 = €37.50.
- Percentage change: Old value €80, new value €92: change = (92−80)/80 × 100 = +15%.
- Result with working: The calculator shows the formula used – ideal for learning.
Practical Examples
Calculate a discount: Regular price €129, 30% off. W = 129 × 0.30 = €38.70. Sale price = 129 − 38.70 = €90.30.
How much cheaper is it? Old price €89, new price €62. p = (89−62)/89 × 100 = 30.3% cheaper.
What was the original price? Now €70 after a 30% discount. G = 70 / 0.70 = €100 was the original price.
Percentage Calculation: All Three Formulas
- Percentage amount: W = G × p ÷ 100
- Base value: G = W × 100 ÷ p
- Percentage rate: p = W × 100 ÷ G
- Percentage change: p = (New − Old) ÷ Old × 100
Frequently Asked Questions (FAQ)
- What is the difference between percentage amount, percentage rate and base value?
- The base value G is the starting value (= 100%). The percentage rate p is the proportion in percent (e.g. 15%). The percentage amount W is the result: W = G × p/100. Example: G = €200, p = 15% → W = €30.
- How do I calculate multiple discounts in a row?
- Don't add them! A 20% and a 10% discount is not 30%. Calculation: €100 × 0.80 × 0.90 = €72 → 28% total discount (not 30%). Percentage reductions multiply – they don't simply add together.
- What does per mille (‰) mean?
- Per mille is one thousandth: 1‰ = 0.1%. Gold content 585‰ = 58.5%. Blood alcohol 1.6‰ = 0.16%. Interest 3.5‰ per month = 0.35%.
