Area Calculator UK 2025

Area

How to Use the Area Calculator

1. Select Shape: Choose the 2D shape you want to calculate from the dropdown menu (square, rectangle, circle, triangle, or trapezoid).
2. Enter Measurements: Input the required measurements in centimetres. Different shapes need different inputs - squares need one side, rectangles need length and width, circles need radius, triangles need base and height.
3. Calculate: Click "Calculate Area" to see your results instantly.
4. View Results: The calculator displays area in square centimetres (cm²) and automatically converts to square metres (m²). For shapes like squares, rectangles and circles, it also shows the perimeter.
5. See Formula: Each result includes the mathematical formula used, helpful for GCSE maths homework and understanding the calculation method.

Area Formulas for 2D Shapes

Square Area

Area = side² (side × side)

A square has all four sides equal. If each side is 5cm, the area is 5 × 5 = 25 cm². The perimeter is 4 × 5 = 20cm. Common in GCSE maths and useful for tile calculations.

Rectangle Area

Area = length × width

Multiply the length by the width. For example, a room 10m long and 5m wide has an area of 50 m². The perimeter is 2 × (10 + 5) = 30m. Essential for flooring, carpet and paint calculations.

Circle Area

Area = π × radius²

The radius is the distance from the centre to the edge. For a circle with radius 5cm, the area is approximately 78.54 cm². The circumference (perimeter) is 2 × π × radius ≈ 31.42cm. Useful for circular ponds, patios or pizza calculations.

Triangle Area

Area = ½ × base × height

The base is any side, and the height is the perpendicular distance from that base to the opposite vertex. For a triangle with base 8cm and height 6cm, the area is ½ × 8 × 6 = 24 cm². Commonly used in GCSE maths and roof calculations.

Trapezoid Area

Area = ½ × (base1 + base2) × height

A trapezoid has two parallel sides of different lengths. Add both parallel sides, multiply by the perpendicular height, then divide by 2. For bases of 8cm and 5cm with height 4cm, the area is ½ × (8 + 5) × 4 = 26 cm².

Complete Guide to Area Formulas and Calculations

Calculating area is one of the most practical mathematical skills you can have. Whether you are measuring rooms for new flooring, planning a garden layout, estimating paint quantities, or helping with GCSE maths homework, understanding how to calculate the area of different shapes is essential. This comprehensive guide covers all the common 2D shapes, their formulas, and practical applications for UK homeowners, students, and professionals.

Additional Area Formulas Beyond the Calculator

While our calculator covers the five most common shapes, here are formulas for additional shapes you may encounter:

Parallelogram

Area = base x height

A parallelogram is a four-sided shape where opposite sides are parallel and equal in length. The height must be measured perpendicular to the base, not along the slanting side. For example, a parallelogram with a base of 12 cm and a perpendicular height of 8 cm has an area of 12 x 8 = 96 cm2. This shape is commonly encountered in roof designs, decorative tiling patterns, and architectural features.

Ellipse (Oval)

Area = pi x semi-major axis x semi-minor axis

An ellipse is an elongated circle with two different radii. The semi-major axis (a) is the longest radius and the semi-minor axis (b) is the shortest. For an ellipse with semi-major axis 10 cm and semi-minor axis 6 cm, the area is pi x 10 x 6 = approximately 188.5 cm2. Ellipses are common in garden design (oval flower beds), architecture (oval windows), and athletics (running tracks).

Rhombus

Area = (diagonal 1 x diagonal 2) / 2

A rhombus is a four-sided shape where all sides are equal but the angles are not necessarily right angles (a square is a special case of a rhombus). If the two diagonals measure 10 cm and 14 cm, the area is (10 x 14) / 2 = 70 cm2. Rhombus shapes appear in diamond patterns on floors, walls, and decorative features.

Regular Hexagon

Area = (3 x sqrt(3) / 2) x side2

A regular hexagon has six equal sides and six equal angles. For a hexagon with side length 5 cm, the area is approximately (3 x 1.732 / 2) x 25 = 64.95 cm2. Hexagons are popular in tile patterns, paving designs, and garden layouts. Many UK garden centres sell hexagonal paving slabs.

Sector (Pie Slice of a Circle)

Area = (angle / 360) x pi x radius2

A sector is a "slice" of a circle defined by its central angle. For a sector with radius 10 cm and an angle of 90 degrees (a quarter circle), the area is (90/360) x pi x 100 = approximately 78.54 cm2. This is useful for calculating the area of curved garden beds, fan-shaped patios, or architectural arches.

Real-World Applications of Area Calculations

Room Measurements and Flooring

When measuring rooms for flooring, carpeting, or tiling, you need to calculate the total floor area. For rectangular rooms, simply multiply length by width. For L-shaped rooms, divide the space into two rectangles, calculate each area separately, and add them together. Most UK flooring is sold by the square metre, so convert your measurements to metres before calculating. Remember to add 10-15% extra for waste and cutting, especially with tiles or patterned materials.

Example: A room measuring 4.5m x 3.2m has an area of 14.4 m2. With 10% waste allowance, order at least 15.84 m2 of flooring. If laminate flooring costs 18 GBP per m2, the material cost would be approximately 285 GBP.

Garden Planning

Accurate area calculations are essential for garden projects including laying turf, spreading gravel, planting beds, and building patios. Turf is typically sold per square metre in the UK, with prices ranging from 3 to 8 GBP per m2 depending on quality. Gravel is usually sold by the tonne, with one tonne covering approximately 12-15 m2 at a depth of 3-5 cm.

Example: A circular patio with a diameter of 4 metres has a radius of 2 metres, giving an area of pi x 4 = approximately 12.57 m2. If paving slabs cost 25 GBP per m2 including labour, the total cost would be around 314 GBP.

Painting and Decorating

To estimate paint quantities, calculate the total wall area to be painted. Measure the length and height of each wall, calculate their areas, and subtract the area of windows and doors. Most UK paint covers 10-12 m2 per litre for the first coat, with better coverage on subsequent coats. For a standard UK room (4m x 3m x 2.4m high), the total wall area is approximately 33.6 m2, minus approximately 3-4 m2 for windows and a door, giving roughly 30 m2 to paint.

Area Unit Conversions

Understanding unit conversions is crucial when working with different measurement systems. Here are the most useful conversions for UK users:

UK Property Measurement Standards

In the UK, property measurements follow specific standards that buyers, sellers, and estate agents should understand:

• RICS Measuring Practice: The Royal Institution of Chartered Surveyors (RICS) sets the standard for property measurement in the UK. Their guidelines specify that floor areas should be measured to the internal face of the perimeter walls, and measurements should be taken at floor level.
• Gross Internal Area (GIA): This is the total floor area measured to the internal face of external walls. It includes stairwells, lifts, and internal walls but excludes external balconies and covered parking. GIA is commonly used for commercial properties and new-build pricing.
• Net Internal Area (NIA): Previously called "usable floor area," NIA excludes common areas, toilets, stairwells, and structural walls. This measurement better represents the actual usable space in a property.
• Estate Agent Measurements: UK estate agents typically use Gross Internal Area when advertising properties. Under Consumer Protection Regulations, floor areas quoted must be accurate and not misleading. However, measurements are often approximate, and buyers should verify with their own surveyor.
• Average UK Room Sizes: A typical UK living room measures approximately 17 m2 (183 ft2), a master bedroom approximately 13 m2 (140 ft2), and a single bedroom approximately 7.5 m2 (81 ft2). UK building regulations require a minimum of 7.5 m2 for a single bedroom and 11.5 m2 for a double bedroom in new-build properties.

Tips for Accurate Area Measurements

• Use a laser measure for large spaces. For rooms over 5 metres in any dimension, a laser distance measure (available from 20-30 GBP) provides more accurate results than a tape measure and can be operated by one person.
• Measure twice, calculate once. Always take at least two measurements of each dimension to verify accuracy. Small errors in measurement are magnified when calculating area.
• Account for irregular shapes. Most real-world spaces are not perfect rectangles. Break irregular rooms into simple shapes (rectangles, triangles), calculate each area separately, then add or subtract as needed.
• Record measurements clearly. Draw a rough floor plan and label each dimension. This makes it much easier to calculate area later and helps when ordering materials or discussing plans with tradespeople.
• Include alcoves and bay windows. When measuring rooms for flooring, include alcoves, bay windows, and other recesses in your total area calculation. These small areas add up and you will need material to cover them.

Frequently Asked Questions

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