The CP Formula in Maths is used to find Cost Price, the original price at which an item is bought. If profit amount is known, CP = SP − Profit, and if loss amount is known, CP = SP + Loss.
In Statistics and quality control, Cp Formula means Process Capability Index: Cp = (USL − LSL) / 6σ.
The CP Formula usually refers to Cost Price Formula in school Maths, especially in profit and loss chapters. Cost price is the amount paid to buy an item, while selling price is the amount received after selling it. Once CP and SP are known, students can calculate profit, loss, profit percentage and loss percentage.
In some advanced Statistics and engineering contexts, Cp refers to the Process Capability Index. This is used to check whether a process can produce results within given limits. For school-level Maths, CP mostly means cost price, while in quality control, Cp means process capability.
Key Takeaways
- CP Formula in Maths: CP = SP − Profit when profit amount is known.
- Loss Case: CP = SP + Loss when loss amount is known.
- Profit Percentage Case: CP = (100 × SP) / (100 + Profit%).
- Loss Percentage Case: CP = (100 × SP) / (100 − Loss%).
- Process Capability Formula: Cp = (USL − LSL) / 6σ.
CP Formula Structure 2026
| Context |
Formula |
Key Use |
| Cost price from profit |
CP = SP − Profit |
When profit amount is given |
| Cost price from loss |
CP = SP + Loss |
When loss amount is given |
| CP with profit percentage |
CP = (100 × SP) / (100 + Profit%) |
When SP and profit% are given |
| CP with loss percentage |
CP = (100 × SP) / (100 − Loss%) |
When SP and loss% are given |
| Process capability |
Cp = (USL − LSL) / 6σ |
Quality control and statistics |
What is CP Formula?
The CP Formula is used to calculate cost price. Cost price is the price at which an article, product or item is bought.
Formula when profit is known:
CP = SP − Profit
Formula when loss is known:
CP = SP + Loss
Where:
- CP = Cost Price
- SP = Selling Price
- Profit = Amount gained
- Loss = Amount lost
If an item is sold for more than its cost price, there is a profit. If an item is sold for less than its cost price, there is a loss.
CP Formula in Maths
In Maths, CP Formula appears in profit and loss questions. It helps students find the original buying price of an item when selling price, profit or loss is given.
Main formulas:
CP = SP − Profit
CP = SP + Loss
For percentage-based questions:
CP = (100 × SP) / (100 + Profit%)
CP = (100 × SP) / (100 − Loss%)
These formulas are useful in Class 7, Class 8, Class 9 and Class 10 commercial mathematics questions.
Cost Price Formula
The cost price formula depends on whether the item is sold at a profit or a loss.
When profit amount is known:
CP = SP − Profit
When loss amount is known:
CP = SP + Loss
When profit percentage is known:
CP = (100 × SP) / (100 + Profit%)
When loss percentage is known:
CP = (100 × SP) / (100 − Loss%)
Cost price calculation becomes easier when students first identify whether the question is based on profit, loss, profit percentage or loss percentage.
CP and SP Formula
CP and SP Formula connects cost price and selling price.
Basic formulas:
Profit = SP − CP
Loss = CP − SP
SP = CP + Profit
SP = CP − Loss
CP = SP − Profit
CP = SP + Loss
Where:
- CP = price at which item is bought
- SP = price at which item is sold
If SP > CP, the result is profit.
If SP < CP, the result is loss.
CP Formula Profit
CP Formula profit is used when an item is sold at a profit. Profit means the selling price is higher than the cost price.
Formula when profit amount is known:
CP = SP − Profit
Example:
If SP = ₹900 and Profit = ₹150, then:
CP = 900 − 150
CP = ₹750
So, the cost price is ₹750.
CP Formula Loss
CP Formula loss is used when an item is sold at a loss. Loss means the selling price is lower than the cost price.
Formula when loss amount is known:
CP = SP + Loss
Example:
If SP = ₹600 and Loss = ₹100, then:
CP = 600 + 100
CP = ₹700
So, the cost price is ₹700.
CP Formula When Profit Percentage is Given
When selling price and profit percentage are given, cost price can be calculated using this formula:
CP = (100 × SP) / (100 + Profit%)
Where:
- CP = cost price
- SP = selling price
- Profit% = profit percentage
Example:
An article is sold for ₹1,200 at a profit of 20%. Find CP.
Formula:
CP = (100 × SP) / (100 + Profit%)
Substitute:
CP = (100 × 1200) / (100 + 20)
CP = 120000 / 120
CP = ₹1000
Answer:
The cost price is ₹1000.
CP Formula When Loss Percentage is Given
When selling price and loss percentage are given, cost price can be calculated using this formula:
CP = (100 × SP) / (100 − Loss%)
Where:
- CP = cost price
- SP = selling price
- Loss% = loss percentage
Example:
An item is sold for ₹800 at a loss of 20%. Find CP.
Formula:
CP = (100 × SP) / (100 − Loss%)
Substitute:
CP = (100 × 800) / (100 − 20)
CP = 80000 / 80
CP = ₹1000
Answer:
The cost price is ₹1000.
Profit and Loss Formula
The profit and loss formula helps students calculate gain or loss in buying and selling situations.
Important formulas:
Profit = SP − CP
Loss = CP − SP
Profit% = (Profit / CP) × 100
Loss% = (Loss / CP) × 100
SP = CP × (100 + Profit%) / 100
SP = CP × (100 − Loss%) / 100
CP = (100 × SP) / (100 + Profit%)
CP = (100 × SP) / (100 − Loss%)
These formulas are used together in cost price calculation and selling price questions.
Profit Percentage Formula
Profit percentage formula is used to find profit as a percentage of cost price.
Formula:
Profit% = (Profit / CP) × 100
Since:
Profit = SP − CP
So:
Profit% = [(SP − CP) / CP] × 100
Example:
If CP = ₹500 and SP = ₹600, then:
Profit = 600 − 500
Profit = ₹100
Profit% = (100 / 500) × 100
Profit% = 20%
Answer:
The profit percentage is 20%.
Loss Percentage Formula
Loss percentage formula is used to find loss as a percentage of cost price.
Formula:
Loss% = (Loss / CP) × 100
Since:
Loss = CP − SP
So:
Loss% = [(CP − SP) / CP] × 100
Example:
If CP = ₹800 and SP = ₹720, then:
Loss = 800 − 720
Loss = ₹80
Loss% = (80 / 800) × 100
Loss% = 10%
Answer:
The loss percentage is 10%.
Cost Price Calculation
Cost price calculation depends on the values given in the question. Students should first identify the case.
| Given Information |
Formula to Use |
| SP and profit amount |
CP = SP − Profit |
| SP and loss amount |
CP = SP + Loss |
| SP and profit% |
CP = (100 × SP) / (100 + Profit%) |
| SP and loss% |
CP = (100 × SP) / (100 − Loss%) |
| SP and discount |
Use marked price and selling price relation first |
Example:
If an item is sold for ₹1500 at 25% profit:
CP = (100 × 1500) / (100 + 25)
CP = 150000 / 125
CP = ₹1200
Process Capability Formula
In Statistics and quality control, CP may also mean Cp or Process Capability Index. This formula measures whether a process can produce output within specified limits.
Formula:
Cp = (USL − LSL) / 6σ
Where:
- Cp = process capability index
- USL = upper specification limit
- LSL = lower specification limit
- σ = standard deviation of the process
The higher the Cp value, the more capable the process is of staying within the specification limits.
Cp Formula Statistics
Cp Formula Statistics is used in quality control, engineering and manufacturing. It compares the allowed spread of a process with the actual spread of the process.
Formula:
Cp = (USL − LSL) / 6σ
Here:
- USL − LSL gives the specification width.
- 6σ represents the natural process spread.
- Cp checks whether the process variation fits within the specification range.
Example:
If USL = 60, LSL = 48 and σ = 2, then:
Cp = (60 − 48) / (6 × 2)
Cp = 12 / 12
Cp = 1
Answer:
The process capability index is 1.
Difference Between CP Formula in Maths and Cp Formula in Statistics
CP Formula can mean different things depending on the subject. In Maths, CP means cost price. In Statistics, Cp means process capability index.
| Basis |
CP Formula in Maths |
Cp Formula in Statistics |
| Full form |
Cost Price |
Process Capability |
| Main use |
Profit and loss |
Quality control |
| Formula |
CP = SP − Profit or CP = SP + Loss |
Cp = (USL − LSL) / 6σ |
| Common in |
School Maths |
Statistics, engineering, manufacturing |
| Main idea |
Buying price of an item |
Process performance within limits |
For school profit and loss chapters, CP usually means cost price.
How to Find CP
To find CP, first check whether the question gives profit amount, loss amount, profit percentage or loss percentage.
Case 1: When SP and profit are given
Use:
CP = SP − Profit
Example:
SP = ₹850
Profit = ₹150
CP = 850 − 150
CP = ₹700
Case 2: When SP and loss are given
Use:
CP = SP + Loss
Example:
SP = ₹900
Loss = ₹100
CP = 900 + 100
CP = ₹1000
Case 3: When SP and profit percentage are given
Use:
CP = (100 × SP) / (100 + Profit%)
Example:
SP = ₹2400
Profit% = 20%
CP = (100 × 2400) / 120
CP = ₹2000
Case 4: When SP and loss percentage are given
Use:
CP = (100 × SP) / (100 − Loss%)
Example:
SP = ₹1800
Loss% = 10%
CP = (100 × 1800) / 90
CP = ₹2000
Solved Examples on CP Formula
CP Formula questions usually test cost price, selling price, profit, loss, percentage and process capability. Read the question carefully to identify whether CP means cost price or Cp means process capability.
Example 1: Find CP when SP and profit are given
Given:
SP = ₹750
Profit = ₹100
Formula:
CP = SP − Profit
Substitute:
CP = 750 − 100
CP = ₹650
Answer:
The cost price is ₹650.
Example 2: Find CP when SP and loss are given
Given:
SP = ₹560
Loss = ₹40
Formula:
CP = SP + Loss
Substitute:
CP = 560 + 40
CP = ₹600
Answer:
The cost price is ₹600.
Example 3: Find CP when SP = ₹960 and profit = 20%
Given:
SP = ₹960
Profit% = 20%
Formula:
CP = (100 × SP) / (100 + Profit%)
Substitute:
CP = (100 × 960) / 120
CP = 96000 / 120
CP = ₹800
Answer:
The cost price is ₹800.
Example 4: Find CP when SP = ₹720 and loss = 10%
Given:
SP = ₹720
Loss% = 10%
Formula:
CP = (100 × SP) / (100 − Loss%)
Substitute:
CP = (100 × 720) / 90
CP = 72000 / 90
CP = ₹800
Answer:
The cost price is ₹800.
Example 5: Find Cp when USL = 110, LSL = 90 and σ = 4
Given:
USL = 110
LSL = 90
σ = 4
Formula:
Cp = (USL − LSL) / 6σ
Substitute:
Cp = (110 − 90) / (6 × 4)
Cp = 20 / 24
Cp = 0.83
Answer:
The process capability index is 0.83.
Common Mistakes in CP Formula
Many CP Formula mistakes happen when students use the same formula for profit and loss cases. The sign changes depending on whether profit or loss is given.
Important checks:
- Use CP = SP − Profit when profit amount is given.
- Use CP = SP + Loss when loss amount is given.
- Use CP = (100 × SP) / (100 + Profit%) when profit percentage is given.
- Use CP = (100 × SP) / (100 − Loss%) when loss percentage is given.
- In Maths, CP usually means cost price.
- In Statistics, Cp usually means process capability index.
- Use Cp = (USL − LSL) / 6σ only for process capability questions.
For profit and loss questions, always identify whether the item is sold at a profit or at a loss before substituting values.
Applications of CP Formula
The CP Formula is useful in Maths, business, trade, statistics and quality control. It helps calculate buying price, selling price, gain, loss and process capability.
Main applications:
- It helps find cost price in profit and loss questions.
- It is used in school Maths commercial arithmetic.
- It helps shopkeepers calculate buying and selling prices.
- It supports profit percentage and loss percentage calculations.
- It helps compare cost price and selling price.
- It is used in discounts, markup and business calculations.
- Cp formula is used in quality control and manufacturing.