Maths in the Garden


Maths in the Garden

This section covers the mathematical skills involved in creating, maintaining, and enjoying a garden.


Flowerbeds come in a range of different shapes, sizes, depths, and heights.

Let's say you wanted to create a rectangular planting area. How would you make sure the corners are correctly placed and angled?

With a ruler and protractor?

These tools work well in most cases. However, gardens are rarely flat enough to accurately use them.

Instead, we can use pegs and strings combined with a basic knowledge of Pythagoras theorem.

Isn't that for triangles?

Yes, it is, but it is also used to create right angles. If the angle is correct, a peg 3 metres along one side and another 4 metres along the other should be 5 metres apart.

An overlay of a 3, 4, 5 triangle to correctly cut a right-angled corner.

The act of digging involves the mechanics of levers and force, especially when you need to remove rocks.

Capacity of buckets or bags is important for moving dirt, along with estimating the total mass - are you able to safely carry it afterwards?


If you are laying a new lawn, you will need to use measurements to calculate how many rolls of turf are required. This can be made more complicated with turf often sold in yards, meaning some conversion is required.

A stack of rolled up turf

Re-seeding a lawn is similar in its usage of measurements and areas to work out how much grass-seed is required.

Mowing lawns also requires some numeracy skills. First, which is the best tool for the job? This is determined by the area of the lawn, distance from the house, and running costs.

Some lawnmowers collect the grass cuttings for disposal, in which case you will also need to consider the capacity when buying and using. How many times will you need to empty it? How can you minimise the distance you need to carry the clippings during the chore?

More power tools than ever, including lawnmowers, are now battery powered. How often will they need recharging? How much of the lawn can be cut in a single charge?

Not many people enjoy mowing the lawn, so we are using decision-based mathematics automatically when planning our route to get the job done as quickly and efficiently as possible.

Paving and Decking

Creating your own paved area is very similar to tiling (Maths in the Bathroom) or flooring (DIY Maths) in its use of mathematics.

Decking has the same maths plus the same mechanics as covered in our DIY Maths section.

flowers planted in gravel

However, if you're planning to gravel an area you also need to take depth into consideration. Instead of simply calculating the area of coverage, you instead need to work out the volume.


After calculating shape, size, and depth, and then using simple mechanics to dig it out, you then need to calculate the amount of pond lining required.

This involves the ability to calculate surface area, as well as how much extra is required at the edges to help pin in in place.

Surely you could just get a massive piece and cut it to size...

You could. However, you are already using maths to estimate what would be classed as more than large enough for the task. Plus, pond lining is sold by the square metre meaning it would be a waste of money.

A square pond in a paved area with a birdbath rising from the centre

Finally, with your pond dug out, it helps to have an idea of the volume it will hold. This is not just to help estimate the cost on a water meter, or how long it will take to fill, but also to assist in choosing number of and types of plants and fish


These come in many different sizes and designs. Therefore, you need to use spatial awareness and measurements to work out which is the best size for purpose and available space.

You also need to consider the placement of the greenhouse to maximise sunlight but to also protect it from strong winds. This involves understanding angles and compass points.

The construction of the greenhouse, if you're doing it yourself, uses the same mathematical skills as covered by the furniture assembly part of our DIY Maths section.

Once a greenhouse is set up, numeracy allows us to maintain a suitable temperature and humidity within the structure to grow your chosen plants.

Walls and Fences

If you wish to build a boundary wall or fence, you will first need to understand plans and maps to make sure you put it in the right place.

Once you know where it is going, you then need to use measurements of length, width, and height to determine how many bricks/stones/panels/posts are required for the job.

How much cement or mortar will be needed? Although this can be bought pre-mixed if it's a long-term project you may instead wish to buy the components to mix yourself as and when you need it. This will minimise wastage but requires a knowledge of ratios.

Basic mechanics are considered when deciding how deep the posts or foundations need to go to support the structure. They also apply to determining height restrictions due to wind.

Determining angles uses basic trigonometry and a knowledge of shapes.


Creating a hedge requires similar skills to building a wall/fence. The main difference being that the hedge needs to be grown in place.

To ensure there are no gaps, you will need to know what size the chosen plant grows to, what height and how deep.

Timing is also a numeracy skill required to work out how long the hedge will take to grow and when to plant it.

A topiary hedge shaped as an elephant

Some people take hedging to a whole different level by creating art works with trees and/or bushes, a practice called topiary.

Like many other artistic creations, this requires a knowledge of shapes, symmetry, spatial awareness, and scaling. On top of this, to ensure the artwork is still alive and fully supported, a good knowledge of mechanics is required.

Outdoor Furniture

The mathematical skills used to build/assemble/paint/treat outdoor furniture are all covered in our DIY Maths section.


Whether you need to provide electricity to a permanent garden feature - like a fountain or patio heater, or to equipment - like lawnmowers or strimmers, the main consideration is cable length.

With permanent features, you will need to make sure there is enough length to reach a suitable plug socket. This may not be a straight line as you may want to hide the cable, prevent people tripping over it, or protect it from accidental damage (for example: running it over with a lawnmower).

For corded power tools, we need to make sure that the cable can reach where we're working. We also need to consider the path it takes to ensure we don't accidentally damage it, trip over it, or pull anything over with it.

Planting Seeds

Growing plants from seed requires us to predict the success rate of growth. It is very easy to plant too many seeds and then not have enough space or pots to move them into as they get bigger.

A knowledge of timing regarding months and seasons is necessary to make sure you are planting at the right time of year. Otherwise, they may not survive and that would be a waste of time and money.

Spatial awareness is a key numeracy skill in the garden. If growing cabbages, they need lots of space on the surface. If growing potatoes, they need lots of space to spread out underground. Parsnips and Carrots would require more depth of soil to grow properly.

Some plants require some mechanics to maintain them. For example, tomato plants can quickly become too heavy with fruit to support themselves and so need to be attached to additional support structures (garden canes or trellises).


a small dog playing with a hose pipe on a lawn

In the garden you may have a watering can, hosepipe and/or water butt.

These items have capacities and/or flow rates that help us decide the best tools and adapters for the task.

Path planning is needed to minimise distance travelled and time taken for a chore. Additionally, if using a hosepipe, the same consideration with this planning is required as with electric cables.

If you wish to fit a water butt to your drainage system, you will need to have spatial awareness regarding a suitable size and measuring skills to link it correctly to the current guttering system.

Chemicals in the Garden

Plant feed, weed-killers, fertilisers, and pest repellents come in various forms.

Some come as concentrated liquids which require watering down with a set ratio of the liquid to water.

Others come in pellets or powders which need to be measured out correctly.

When using some of these you may need to consider timing for when is best to use them.

Garden Games

There are lots of different garden games. All of them will involve some form of mathematics/numeracy.

We've covered some of these in our page on Maths in the Living Room.

What about just kicking a football around?

A football being kicked towards a goal

There is a lot of mathematics in sport. Everything from game theory through to mechanics and physics.

For example, footballers are applying very advanced mathematics to their gameplay without even realising it. How much force to hit the ball with; what angle to apply the kick at; spatial awareness of other players, the ball, and the goals; player statistics; team positioning; and much more.

Maths in Nature

There are a lot of fascinating applications of mathematics within nature.

These includes fractals, spirals, symmetry, and sequences.

For example: The Fibonacci sequence of numbers (1, 1, 2, 3, 5, 8, 13 ...) links in with the nature of many living things. Whether it's the number of petals on a flower or the number of spirals on a pinecone or pineapple.

a layer of pinecones with an autumnal leave on top

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