Example 1
- a = 5
- b = 3
16
What is 5² − 3²? 16. (5 − 3)(5 + 3) = 2 × 8.
Difference of squares calculator
Type a and b. The difference of squares is a² − b², written as the product (a − b)(a + b). 5 and 3 give 16. 10 and 6 give 64. 5 and 5 give 0.
The calculator multiplies (a − b)*(a + b). It does not compute a*a − b*b on its own. 5 and 3 give 16, because 2 × 8.
Results
Enter data and click Calculate.
How it works
The difference of squares of two numbers is a² − b². That is the same product (a − b)(a + b). With 5 and 3 you have 2 × 8 = 16. The calculator does not square a and b separately: it multiplies the difference by the sum.
The fields are a and b. 10 and 6 give 64, because 4 × 16. When a = b the difference is zero and the product is 0. 5 and 5 give 0. That is not an error, only equal squares.
Order matters. 3 and 5 give −16, because (3 − 5)(3 + 5) = (−2) × 8. A minus in the result is the sign, not a message.
Square of a sum is on the neighbouring page and computes (a + b)², not a difference. A power with exponent 2 raises one number.
The header units switch does not multiply anything. 5 and 3 stay 16 whatever the label says.
5 and 3 give 16. 10 and 6 give 64. 5 and 5 give 0. That is the whole card: a product of difference and sum.
Formula
a² − b² = (a − b)(a + b)
How to use
- Type a and b, for example 5 and 3.
- Click Calculate. The difference of squares comes out 16.
- 10 and 6 give 64. 5 and 5 give 0.
- 3 and 5 give −16, because the order of a and b matters.
- Square of a sum lives on the neighbouring card.
5 and 3 give 16
The difference of squares is (a − b)(a + b). 5 and 3 give 16. 10 and 6 give 64. 5 and 5 give 0.
- difference
- a² − b². 5 and 3 give 16. 5 and 5 give 0, because the squares cancel.
- squares
- Two squares a² and b². The calculator does not power them apart; it multiplies (a − b)(a + b).
- product
- Difference times sum. 10 and 6 give 64, because 4 × 16.
Examples
Example 2
- a = 10
- b = 6
64
What is 10² − 6²? 64. 4 × 16.
Example 3
- a = 5
- b = 5
0
What is 5² − 5²? 0. Equal squares, a zero difference.
Related calculators
Common questions
What is 5² − 3²?
16. (5 − 3)(5 + 3) = 2 × 8. The calculator multiplies difference by sum.
What does difference of squares mean?
a² − b², the same product (a − b)(a + b). Two squares, one difference.
What do 10 and 6 give?
64. 4 × 16. That is 100 − 36.
What do 5 and 5 give?
0. Equal a and b, a zero difference, a zero product.
Does the order of a and b matter?
Yes. 3 and 5 give −16. 5 and 3 give 16.
Does a negative b pass?
Yes. 5 and (−3) give 16, because (5 − (−3))(5 + (−3)) = 8 × 2.
How is this different from the square of a sum?
Here a² − b². There (a + b)². Neighbouring cards, another formula.
Does the calculator compute a*a − b*b?
No. It multiplies (a − b)*(a + b). The result is the same.
Where is the square of one number?
On the power page. Here you always have two fields and a product.
Does a comma in 5.5 work?
Yes. 5.5 and 5,5 are the same decimal.
Knowledge sources
The calculator computes the same formula as the definition below.
Page updated in 2026.