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How can I easily cut a thick paving slab/flag-stone to the size I need without specialised tools?

The slab is around 2 inches thick, and very heavy.

They are similar to the image below.

Decorative patio paving slabs

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A heavy hammer (3-4 lb head) and a broad cold chisel are the only really sensible way to cut a stone that heavy, short of industrial tools, and I don't know that I'd call them specialized -- but you can buy them cheaply at an import tool store or home improvement "big box". The only practical alternative is a saw or angle grinder with a carbide or diamond wheel mounted, and this is much noisier and more expensive, not to mention a dry saw produces huge volumes of dust you shouldn't inhale.

To cut, just use the hammer and chisel to score a line a few millimeters deep where you want the cut, then put a rod (shovel handle works) under the cut line, and stand with your feet on either side of the cut line, as far from the line as the stone will allow. If necessary, have a helper tap near your feet with the hammer, or stike the chisel in the precut groove. The stone will break pretty cleanly at the scored line, and you can clean up any remaining irregularities easily with the chisel.

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    This is how I have cut natural slabs like shale and slate. This is how they did it for thousands of years. – Robert Cartaino Apr 25 '16 at 21:26
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If the material is too thick for Zeiss' method (which works really well), you can move up to the next level of cutting/breaking rock. You will need an impact hammer, a sledge hammer (or other very heavy headed hammer), and some metal wedges (steel works best).

Using the impact hammer, drill holes along the axis of where you want the rock to break. The depth of the holes will depend on the material you are separating, and other factors, like how much of the rock is covered or buried. After drilling the holes, insert two wedges against the side of the holes. Insert a third wedge between them. Striking the third wedge into the rock will start a crack formation. Repeat in the other hole.

This method should work well for most large garden sized rocks. This method is not good for very small rocks (maybe less than a 1 inch (~2 centimeters) diameter).

Here's a video demonstrating this method.

Wikipedia also has a much more detailed description of the process with pictures.

Plug and feather, also known as plugs and wedges, feather and wedges, wedges and shims, pins and feathers and feather and tare, refers to a technique and a three-piece tool set used to split stone.

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An angle grinder with a cutting wheel works, and is less likely to break the slab than the hammer and chisel method.

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No electrical outlets around?
A star drill along with a cold-steel chisel and hammer will work even if the stone is still in the ground. The star drill works like a chisel but you turn the drill after each blow to create a round hole. After a few pilot holes aligned along the line you wish to split the piece, the chisel between the holes will cleave the stone.
Take your time.
Put lemonade into the fridge to cool for when you finish…
and…
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