Quick answer
The area of a parallelogram is A = base × height. With base 8 and height 3 the area is 24.
Enter the base and the perpendicular height. The calculator returns the area.
Related tools: Area Calculator: Area of common two-dimensional shapes. Area of a Circle Calculator: Area of a circle from its radius, diameter or circumference. Area of a Trapezoid Calculator: Area of a trapezoid from its parallel sides and height.
How to use the Parallelogram Area Calculator
- Enter base (above 0).
- Enter height (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Base | A number | > 0 |
| Height | A number | > 0 |
Formula and method
Formula
A = b × h
IEEE-754 double precision; shown to at most 6 decimal places.
Base times perpendicular height.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Base = 8; Height = 3.
| Result | Value |
|---|---|
| Area | 24 |
Example 2
Inputs: Base = 2.5; Height = 2.
| Result | Value |
|---|---|
| Area | 5 |
The first line is the headline result (area). IEEE-754 double precision; shown to at most 6 decimal places.
Height, not side
The height is measured perpendicular to the base, not along the slanted side. A parallelogram can be cut and rearranged into a rectangle of the same base and height, which proves the formula.
Other formulas
If you know two sides a, b and the angle θ between them, the area is ab·sin θ. For a rhombus with diagonals p and q it is pq ÷ 2. All values must be positive.
Perpendicular height, not the slanted side
The height is the perpendicular distance between the two parallel sides. With base 8 and height 3 the area is 24. Using a slanted side of 5 instead of the height would give 40, which is wrong.
A parallelogram has the same area as a rectangle with the same base and height, because the slanted end can be cut off and moved to the other side. Equal areas do not mean equal perimeters, since the slanted sides can be longer.
How the result changes with base
Holding every other input at the first worked example, this table changes only base. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Base | Area |
|---|---|
| 4 | 12 |
| 8 | 24 |
| 16 | 48 |
| 32 | 96 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Base: entering "0" shows "Base must be greater than 0." beside that field and no result.
Choosing between the Parallelogram Area Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Area Calculator](/math/area-calculator/) | shape and a | Area |
| [Area of a Circle Calculator](/math/area-of-a-circle/) | i know the and value | Area |
| [Area of a Trapezoid Calculator](/math/area-of-a-trapezoid/) | base a, base b and height | Area |
| [Surface Area Calculator](/math/surface-area-calculator/) | shape and a | Surface area |
| [Triangle Area Calculator](/math/triangle-area-calculator/) | base and height | Area |
Background: geometry measurements
Geometry results carry units that depend on the quantity: a perimeter or length is in linear units such as cm, an area or surface area is in square units (cm²) and a volume is in cubic units (cm³). Use one length unit for every input, because the calculator multiplies the numbers as given.
Flat (2D) shapes have an area and a perimeter; solids (3D) have a surface area and a volume. Two familiar checks: a circle of radius r has area πr² and circumference 2πr, and a sphere has volume (4/3)πr³ and surface area 4πr².
Assumptions and limitations
- Positive values
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for base to confirm this.
Frequently asked questions
What is the area with sides 5 and 8 at 30°?
20, since 5 × 8 × sin 30°.
Is a rectangle a parallelogram?
Yes, with a 90° angle.
How do I find the height?
Use side × sin of the angle.
Why is the area not base times the slanted side?
Because the slanted side is longer than the perpendicular height. Only the perpendicular height measures how far apart the parallel sides are.
Do two parallelograms with the same area have the same perimeter?
Not necessarily. A base of 8 with height 3 and a base of 6 with height 4 both have area 24, but their perimeters depend on the slant.
What does the Parallelogram Area Calculator calculate?
Area of a parallelogram. It returns Area.
What formula does the Parallelogram Area Calculator use?
A = b × h. Base times perpendicular height.
What do I need to enter in the parallelogram Area Calculator?
You enter Base and Height.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Positive values.
What is an example of a parallelogram Area result?
With base 8 and height 3, the area is 24.
Related calculators
- Area Calculator — Area of common two-dimensional shapes.
- Area of a Circle Calculator — Area of a circle from its radius, diameter or circumference.
- Area of a Trapezoid Calculator — Area of a trapezoid from its parallel sides and height.
- Surface Area Calculator — Surface area of a sphere, cube, cylinder, cone or box.
- Triangle Area Calculator — Area of a triangle from base and height.
- Sector Area Calculator — Area and arc length of a circular sector.
- Square Area Calculator — Area of a square.
Sources
- OpenStax, Algebra and Trigonometry 2e (Rice University): exponents, radicals, logarithms and inverse trigonometric functions
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.