Loss Percentage Formula
You bought a laptop for $600 and later sold it for $450. The $150 you lost is easy to see – but how do you express that loss as a percentage of what you originally paid? That is where the loss percentage formula comes in.
What Is the Loss Percentage Formula?
Loss % = (Loss ÷ Cost Price) × 100
Before using it, you first need the absolute loss value:
Loss = Cost Price (CP) − Selling Price (SP)
This formula applies whenever the selling price is lower than the cost price. If SP is higher than CP, the transaction results in a profit, not a loss.
Two quick definitions:
- Cost Price (CP) – the amount paid to acquire or produce an item.
- Selling Price (SP) – the amount received when the item is sold.
How to Calculate Loss Percentage Step by Step
- Find the cost price of the item.
- Find the selling price of the item.
- Calculate the loss: Loss = CP − SP.
- Divide the loss by the cost price.
- Multiply by 100 to get the percentage.
Solved Examples
Example 1 – Basic Calculation
A store purchased a batch of headphones for $800 and sold them for $640.
- CP = $800, SP = $640
- Loss = 800 − 640 = $160
- Loss % = (160 ÷ 800) × 100 = 20%
The store incurred a 20% loss on the headphones.
Example 2 – Finding the Selling Price
A merchant marks a product at a cost price of $250 and wants to know what selling price corresponds to a 12% loss.
- Loss = 12% of 250 = $30
- SP = 250 − 30 = $220
Alternatively, use the shortcut formula:
SP = CP × (100 − Loss%) ÷ 100 → 250 × 88 ÷ 100 = $220
Example 3 – Finding the Cost Price
An item was sold for $510 at a 15% loss. What was the original cost?
CP = SP × 100 ÷ (100 − Loss%)
CP = 510 × 100 ÷ 85 = $600
Example 4 – Comparing Two Losses
A shopkeeper sells two televisions.
| TV A | TV B | |
|---|---|---|
| Cost Price | $1,200 | $300 |
| Selling Price | $1,080 | $270 |
| Loss | $120 | $30 |
| Loss % | (120 ÷ 1200) × 100 = 10% | (30 ÷ 300) × 100 = 10% |
Even though TV A lost $120 and TV B lost only $30, both transactions had the same 10% loss – demonstrating why percentage matters more than absolute value when comparing deals of different sizes.
Related Formulas at a Glance
| What you need | Formula |
|---|---|
| Loss | CP − SP |
| Loss % | (Loss ÷ CP) × 100 |
| SP at a known loss% | CP × (100 − Loss%) ÷ 100 |
| CP at a known loss% | SP × 100 ÷ (100 − Loss%) |
| Profit % (for reference) | (Profit ÷ CP) × 100 |
Profit Percentage vs. Loss Percentage
Both formulas share the same structure – the difference is the direction of the transaction:
- Profit % = (SP − CP) ÷ CP × 100 – used when SP > CP
- Loss % = (CP − SP) ÷ CP × 100 – used when SP < CP
In both cases the base (denominator) is always the cost price, never the selling price. Using the wrong base is the most common mistake students and analysts make when working with profit-and-loss problems.
Common Mistakes to Avoid
- Using SP instead of CP as the base. The cost price is always 100% in standard commerce calculations.
- Confusing loss with loss percentage. A $50 loss on a $100 item is 50%; the same $50 loss on a $1,000 item is only 5%.
- Reporting a negative loss percentage. If the formula yields a negative number, the transaction is actually a profit – switch to the profit percentage formula.
This article covers standard arithmetic loss percentage calculations as taught in commerce and basic mathematics. For investment or accounting contexts, consult a financial professional.