Profit and loss percentage formula

Profit and loss percentage formulas

Profit and loss percentages are worked out on the cost price (CP), the price you paid. The selling price (SP) is what you sold for.

Profit = SP − CP, and profit % = profit ÷ CP × 100

Loss = CP − SP, and loss % = loss ÷ CP × 100

This is the convention in school maths and most exam questions: unless a question says otherwise, divide by the cost price. Businesses also use a second measure, the margin, which divides by the selling price. Both are covered below.

Worked examples

When you buy several items and sell them separately, add up all the costs and all the sales first. A trader who buys 50 shirts at ₹220 each (₹11,000) and sells them at ₹275 each (₹13,750) makes ₹2,750, which is 25% of the cost.

Selling price from a profit or loss percentage

To make a given profit, multiply the cost price by 1 plus the percentage as a decimal:

SP = CP × (1 + profit % ÷ 100)

SP = CP × (1 − loss % ÷ 100)

• Bought for $60, want 35% profit: 60 × 1.35 = $81.
• Bought for ₹900, sold at a 20% loss: 900 × 0.80 = ₹720.

Cost price from the selling price

When you know what something sold for and the percentage made, divide instead:

CP = SP ÷ (1 + profit % ÷ 100)

CP = SP ÷ (1 − loss % ÷ 100)

• Sold for ₹1,380 at 15% profit: 1,380 ÷ 1.15 = ₹1,200. The profit was ₹180.
• Sold for $51 at a 15% loss: 51 ÷ 0.85 = $60. The loss was $9.

Taking 15% off ₹1,380 gives ₹1,173, which is wrong: the 15% was worked out on the cost, not on the selling price.

Profit margin and markup

In business, the same profit is often described two ways. Markup is the profit percentage from school maths. Margin divides by the selling price, so it is always the smaller number.

Markup % = profit ÷ cost × 100

Margin % = profit ÷ selling price × 100

An item that costs $40 and sells for $50 has a $10 profit: a 25% markup and a 20% margin.

To convert, margin = markup ÷ (1 + markup) and markup = margin ÷ (1 − margin), with both as decimals. A 50% margin needs a 100% markup: doubling the cost.

Gross profit margin, the figure on a company’s accounts, is the same idea for a whole business: revenue minus the direct cost of what was sold, divided by revenue. If you are setting prices, decide which one you mean before agreeing a target such as “30%”.

Profit after a discount

Shops mark a price up from the cost, then sometimes take a discount off the marked price. Work it through one step at a time:

A 40% markup and a 15% discount don’t leave 25% profit, because the discount is taken from the bigger, marked-up price. Multiplying the steps gives the answer in one go: 1.40 × 0.85 = 1.19, a 19% profit. The discount calculator works out the sale price from the marked price.

Profit along a chain of sellers

When goods pass from a maker to a wholesaler to a shop, each adds its own profit on what it paid. The percentages multiply rather than add:

The customer pays 825 ÷ 500 = 1.65 times the maker’s cost, 65% more, not 10 + 20 + 25 = 55%. To find the maker’s cost from the shop price, divide back through each step: 825 ÷ 1.25 ÷ 1.20 ÷ 1.10 = ₹500.

Two items sold at the same price

A classic exam question: two phones are each sold for ₹9,600, one at a 20% profit and the other at a 20% loss. Is it break-even? No.

• Phone 1 cost 9,600 ÷ 1.20 = ₹8,000, a profit of ₹1,600.
• Phone 2 cost 9,600 ÷ 0.80 = ₹12,000, a loss of ₹2,400.
• Overall: ₹20,000 spent and ₹19,200 received, a loss of ₹800, which is 4% of ₹20,000.

Whenever two items sell for the same price at the same percentage profit and loss, the result is always a loss of (percentage²) ÷ 100 percent: here 20 × 20 ÷ 100 = 4%.

Profit after expenses

In exam questions, extra costs such as transport or repairs are usually added to the cost price before you work out the percentage:

Measured against the ₹6,000 purchase price alone, the same sale would look like a 50% profit, which overstates it. For a small business, the same thinking applies to fees, packaging and delivery: include every cost of getting the item sold before you decide whether a price is profitable.

A useful check is the break-even price, the selling price that gives zero profit. It is simply the total cost price, ₹7,500 here. Anything above it is profit; anything below it is a loss.

Profit and loss in Excel or Google Sheets

With the cost price in A2 and the selling price in B2:

A negative result from the first two formulas is a loss. Copy them down a column to check a whole stock list in one go.

Common mistakes

• Dividing by the selling price. That gives the margin. School and exam questions want the cost price underneath unless they say otherwise.
• Treating markup and discount as opposites. 25% up and 25% down leaves you 6.25% below where you started.
• Leaving out costs. Delivery, repairs or fees paid to buy something are part of the cost price if the question includes them.
• Calling a discount a loss. Selling at 15% off the marked price is only a loss if the sale price falls below the cost price. Work out the profit or loss against the cost, not the marked price.
• Rounding the cost price. In reverse questions, keep the exact cost price until the end. Rounding ₹1,173.91 to ₹1,174 before working out a percentage can shift the answer.
• Averaging percentages. A 10% profit on a $50 item and a 30% profit on a $500 item isn’t a 20% profit overall. Add the money up: $5 + $150 = $155 on $550, which is 28.2%.