📏 Enter known values

📐 Accepted units: mm, cm, dm, m, dam, hm, km, in, ft, yd, mi

Formula Reference

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Worked example

Data
Base
\(b = {\color{#6c5ce7}{6\,\text{cm}}}\)
Height
\(c = {\color{#6c5ce7}{4\,\text{cm}}}\)
Perimeter
\(a = \,?\)
Formula
\[a = 2\cdot{b}+2\cdot{c}\]
Steps
1Substitute the values
\[a = 2\cdot{\color{#6c5ce7}{6\,\text{cm}}}+2\cdot{\color{#6c5ce7}{4\,\text{cm}}}\]
Each letter is replaced by its value.
2Multiply
\[a = 12\,\text{cm}+8\,\text{cm}\]
\(2\cdot6 = 12\)\(2\cdot4 = 8\)
3Add
\[a = 12\,\text{cm}+8\,\text{cm} = 20\,\text{cm}\]
\(12+8 = 20\)
Perimeter: 20 cm
Check

If we use the result to calculate Base, we should get the value you entered:

\[b = \frac{{a}-2\cdot{c}}{2}\]
\[b = \frac{20\,\text{cm}-2\cdot4\,\text{cm}}{2} = 6\,\text{cm}\]
It gives 6 cm, the same as the value entered.
Calculate the Perimeter
Please fill in the fields:
Base Height
And leave empty
Perimeter
Calculate the Base
Please fill in the fields:
Perimeter Height
And leave empty
Base
Calculate the Height
Please fill in the fields:
Perimeter Base
And leave empty
Height

How to calculate the perimeter of a rectangle

The perimeter is the total length of the border of a figure. A rectangle has two pairs of equal sides, the base and the height, so its perimeter is:

\[ P = 2 \times \text{Base} + 2 \times \text{Height} = 2 \times (\text{Base} + \text{Height}) \]

If you know the perimeter and one side, the other side is half the perimeter minus the known side:

\[ \text{Base} = \frac{P}{2} - \text{Height} \]

\[ \text{Height} = \frac{P}{2} - \text{Base} \]

How to use the calculator

  1. Enter two of the three values: the perimeter, the base and the height.
  2. Leave empty the one you want to find.
  3. Press Calculate. The perimeter is a length, so it is in the same unit as the sides (cm, m, ft), not squared.

Worked examples

1. Rectangle of 8 cm by 5 cm

\[ P = 2 \times 8 + 2 \times 5 = 26\ \text{cm} \]

2. Height of a rectangle with a perimeter of 30 m and a base of 9 m

\[ \text{Height} = \frac{30}{2} - 9 = 6\ \text{m} \]

3. Fencing a garden

A garden is 12 m long and 7.5 m wide. The fence needs \( 2 \times (12 + 7.5) = 39 \) m. If the gate takes up 1 m, buy 38 m of mesh plus the gate.

4. Baseboard for a room

A room of 4.2 m by 3.6 m has a perimeter of \( 2 \times (4.2 + 3.6) = 15.6 \) m. Subtract the width of the door (for example, 0.8 m) and you need 14.8 m of baseboard.

Perimeter and area are different

The perimeter measures the border and the area measures the surface inside. Two rectangles with the same perimeter can have very different areas. All these rectangles have a perimeter of 24:

BaseHeightPerimeterArea
1112411
1022420
932427
842432
752435
662436

For a fixed perimeter, the square (6 × 6) has the largest area.

When Do You Need to Calculate the Perimeter of a Rectangle?

🏡 Fencing a Yard or Garden

Fences, hedges and garden edging are sold by length. The perimeter of a rectangular yard tells you how many meters or feet to buy, minus the width of the gates.

Avoids buying too much or too little fencing
🧱 Baseboards and Trim

Baseboards, crown molding and edge trim go around the border of a room. The perimeter, minus the doors, is the length you need.

Quick material list for finishing a room
🖼️ Picture Frames

A frame goes around the four sides of a picture. The perimeter of the picture plus an allowance for the mitered corners gives the length of molding to cut.

Cut frames without wasting molding
🏃 Running Laps

When you walk or run around a rectangular field or block, each lap is its perimeter. Dividing a target distance by the perimeter gives the number of laps.

Plan distances for training
💡 Decoration and LED Strips

LED strips, string lights and ribbons around tables, mirrors or ceilings are measured by the perimeter of the rectangle they outline.

Buy the right length of strip and power supply
📚 School Exercises

Perimeter problems teach the difference between length and surface. Many exercises give the perimeter and one side and ask for the other.

Practice with simple equations

Common Mistakes

⚠️ Adding Only Two Sides
Common Error: Adding the base and the height once: 8 + 5 = 13 instead of 26. A rectangle has four sides.
✅ Solution: P = 2 × (base + height)
⚠️ Multiplying the Sides
Common Error: Using base × height, which is the area, not the perimeter.
✅ Solution: The perimeter adds lengths; the area multiplies them
⚠️ Square Units
Common Error: Writing the perimeter in cm² or m². The perimeter is a length.
✅ Solution: Use the same unit as the sides: cm, m, ft
⚠️ Forgetting to Halve When Solving
Common Error: To find a side, subtracting the other side from the whole perimeter: 30 − 9 = 21 instead of 30 ÷ 2 − 9 = 6.
✅ Solution: Divide the perimeter by 2 before subtracting
⚠️ Mixed Units
Common Error: A base in meters and a height in centimeters. 3 m + 50 cm is not 53.
✅ Solution: Convert both sides to the same unit
⚠️ Not Discounting Openings
Common Error: When buying baseboard or fencing, using the full perimeter even though doors and gates interrupt it.
✅ Solution: Subtract the width of doors and gates

Applications by Industry

Construction & Renovation
  • Foundations: Length of formwork for rectangular footings
  • Trim: Baseboards, crown molding and edge profiles
  • Fencing: Perimeter fences for lots and building sites
Landscaping & Agriculture
  • Garden beds: Edging for rectangular beds
  • Livestock: Electric fence around paddocks
  • Irrigation: Drip line around the edge of a field
Interior Design
  • Rugs: Binding tape for the edges of a rug
  • Lighting: LED strips around ceilings and furniture
  • Curtains: Trim for rectangular windows
Manufacturing
  • Frames: Molding for picture and window frames
  • Sheet metal: Edge length to weld or seal
  • Gaskets: Rubber seals around rectangular doors and lids
Sports
  • Fields: Boundary lines and fences of rectangular pitches
  • Training: Laps around a field to reach a distance
  • Courts: Line paint for basketball and tennis courts
Education
  • Geometry: The difference between perimeter and area
  • Algebra: Solving for a side with simple equations
  • Optimization: The largest area for a given perimeter

External Resources

Other calculators

Perimeter of a Rhombus
Perimeter of a Rhombus
Perimeter of a Square
Perimeter of a Square
Perimeter of a Trapezoid
Perimeter of a Trapezoid
Perimeter of a Triangle
Perimeter of a Triangle
Perimeter of a Circle
Perimeter of a Circle
Perimeter of a Rhomboid
Perimeter of a Rhomboid
Circle Calculator
Circle Calculator
Surface Area of a Cylinder
Surface Area of a Cylinder

Geometry Calculators

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