Each change creates a new base

With successive percentage changes, the next rate acts on the amount left by the previous step. That is why adding rates usually fails. Use multipliers to keep track of the changing base.

Two discounts

Start with 200. A 20% discount multiplies it by 0.80, giving 160. A further 10% discount multiplies 160 by 0.90, giving 144. The total saving is 56 out of 200, or 28%.

200 × 0.80 × 0.90 = 144

An increase followed by a decrease

Increase 100 by 20% to get 120. Then reduce 120 by 20% to get 96. The net change is a 4% decrease. Equal percentage rates do not cancel because they apply to different amounts.

Formula for successive percentage changes

Convert an increase of p% to 1 + p/100 and a decrease to 1 − p/100. Multiply the starting amount by every multiplier in sequence. Subtract 1 from the product of the multipliers and multiply by 100 to find the net percentage change.

Net change = (multiplier₁ × multiplier₂ − 1) × 100

Does the order matter?

For pure percentage multipliers without intermediate rounding, the final product is unchanged when the order changes. However, a fixed-amount coupon, eligibility rule, tax treatment or rounding at each step can change a real checkout total. Do not assume the simple model captures every store policy.

Round at the right point

Keep the full intermediate amount for mathematical comparisons. For actual transactions, use the merchant’s stated rounding rule. Small rounding differences can accumulate across many repeated steps.

Put the method into practice

Choose the percentage calculator for parts and wholes, or use the percentage change calculator for movement from an original value. For a sale price, the discount calculator and reverse percentage calculator answer two different questions.

Questions to check before calculating

Which number is the reference?

Identify the whole or original amount before calculating. If neither value is the natural reference, consider whether a mean-based percentage difference fits your question.

Should I round intermediate values?

For a mathematical result, keep intermediate precision and round the final display. Actual transaction rules may require a particular rounding policy.

Can I use this as an official grade or financial determination?

These guides explain arithmetic. Institutional grading rules, financial policies and legal requirements must be checked separately.

Take the formula with you

Write the question in words, label the known values and choose the denominator deliberately. Check the answer with an estimate or by reversing the calculation. A short explanation alongside the number makes the result easier to understand and less likely to be misused.