Profit and Loss Calculator
Enter what it cost and what it sold for. This gives the profit or loss in money and as a percentage of the cost price.
Profit
25%
- Profit
- $100.00
- Cost price
- $400.00
- Selling price
- $500.00
- As a percentage
- 25%
- Bought for $400.00 and sold for $500.00, which is a profit of $100.00.
- The percentage is always taken on the cost price, not the selling price. That is the convention the syllabus uses, and it is the single most common place to lose a mark on this topic.
- It is why the same amount is a different percentage each way round. A gain of 100 on a cost of 400 is 25%; a loss of 100 on a cost of 500 is 20%.
About profit and loss
Two prices decide everything here. The cost price is what an item was bought or made for; the selling price is what it went for. If the selling price is higher there is a profit, and if it is lower there is a loss.
The amount is a subtraction and nobody gets that wrong. The percentage is where the marks go, because it is always taken on the cost price — never on the selling price. Buy for 400 and sell for 500 and the profit is 100, which is 25% of the 400 it cost.
That convention is why the same gap gives a different percentage each way round. A profit of 100 on a cost of 400 is 25%; a loss of 100 on a cost of 500 is 20%. The money is identical and the percentages are not, because the number being divided by changed.
It is also why a 25% profit and a 25% discount do not cancel out. Adding 25% to 400 gives 500; taking 25% off 500 gives 375, not 400 — because the second percentage was of a larger number. Percentages are never reversible by simply applying them backwards.
What it works out
- Profit or loss as an amount
- The percentage, taken on the cost price
- Which of the two it is
- Any pair of prices
The formula
Profit = SP − CP Profit % = Profit × 100 ÷ CP
Subtract the cost price from the selling price. If the answer is positive it is a profit; if it is negative it is a loss, and the size of the loss is that answer without its sign.
Bought for $400 and sold for $500, the profit is $100. As a percentage that is 100 × 100 ÷ 400 = 25%.
The divisor is always the cost price. Dividing by the selling price instead would give 20%, which is a different and wrong answer to this question — and it is the single most common mistake on the topic.
The same rule applies to a loss. Bought for $500 and sold for $400 is a loss of $100, and 100 × 100 ÷ 500 = 20%. Notice that the same $100 is 25% one way and 20% the other, purely because the cost price changed.
Rearranging gives the other questions. To find the selling price from a target profit percentage, SP = CP × (100 + Profit %) ÷ 100. To find the cost price from a known selling price and percentage, CP = SP × 100 ÷ (100 + Profit %).
- CP
- Cost price — what it was bought or made for. Always the number you divide by.
- SP
- Selling price — what it went for.
- Profit %
- The profit as a percentage of the cost price.
A worked example
Something bought for $400 and sold for $500.
That works out to 25 %.
- Profit
- $100.00
- Cost price
- $400.00
- Selling price
- $500.00
- As a percentage
- 25%
Questions
How do you calculate profit percentage?
Divide the profit by the cost price and multiply by 100. A $100 profit on a $400 cost is 25%.
Is the percentage on cost price or selling price?
Cost price, always, in this topic. Dividing by the selling price gives a different figure — 20% instead of 25% on these numbers — and is the most common mistake made here.
How do you calculate loss percentage?
The same way. Divide the loss by the cost price and multiply by 100. A $100 loss on a $500 cost is 20%.
How do I find the selling price for a given profit?
SP = CP × (100 + Profit %) ÷ 100. To make 25% on a cost of $400, sell at 400 × 125 ÷ 100 = $500.
How do I find the cost price from the selling price?
CP = SP × 100 ÷ (100 + Profit %). Sold at $500 with a 25% profit, the cost was 500 × 100 ÷ 125 = $400.
Why do a 25% profit and a 25% discount not cancel?
Because the second percentage is of a bigger number. Adding 25% to 400 gives 500; taking 25% off 500 gives 375. Percentages cannot be undone by applying them in reverse.
What is the difference between profit and margin?
Profit percentage here is on the cost price, which businesses call markup. Margin is the same profit as a share of the selling price, so it is always the smaller of the two — a 25% markup is a 20% margin.
What is overhead or cost price meant to include?
Whatever it genuinely cost to get the item ready to sell — the purchase price plus transport, repairs and any other expense. Questions usually say to add those to the cost price before working anything out.