You'll need a pump any time you puncture or change a tyre. That won't be very often. More commonly, you'll use a pump to keep your tyres topped up to the right pressure. That's because air slowly seeps out of even intact innertubes.
The thinner and higher pressure the tyre is, the more often you'll need to add air. Every two or three weeks might be fine for a 50mm mountain bike tyre, whereas a 23mm racing tyre might need topping up every two or three days. Many cyclists don't do this and ride around on tyres that are too soft. That vastly increases the risk of punctures. It also increases rolling drag – and thus pedalling effort – and compromises the handling of the bike.
Bike tyres have a pressure rating stamped on the sidewall in either psi (pounds per square inch) or bar (barometric, or atmospheric, pressure). One bar equals 14.5psi. Whichever measurement you prefer, try to keep your bike's tyres inflated within the tyre's recommended range. Towards the bottom of the range is okay for lightweight cyclists, while heavyweight cyclists should aim for the higher figure.
It's well worth buying a pump with a pressure gauge so that you can judge accurately how firm your tyres are. And as you'll be using the pump often, it pays to get one that's easy to use. That means a floor pump of some kind. Pushing a pump down against the floor uses half the energy of pushing a pump against your other hand. It's the only practical way for more slightly built cyclists to inflate higher pressure tyres properly – and it's much easier for everybody.
The most efficient floor pumps are big T-shaped models that are also called track pumps. They pump a lot of air per stroke and almost always come with a gauge. Their only disadvantage is that they're too big and awkward to carry on a bike. So you will need a portable pump as well – or if money or space is tight, instead.
As a rule of thumb, the smaller and lighter a pump is, the more time-consuming and difficult it is to use to inflate your tyres. The 'maximum pressure' figure quoted for mini-pumps is the pressure they can reach before the pump gives up (i.e. fails), not before you give up! If your portable pump is strictly for emergencies and you're strong enough (and strong willed enough!) to use it, then a sub-100g pump the size of fat cigar might suffice. If you need a portable pump that's easy to use, on the other hand, get something bigger.
Whatever pump you buy, make sure that the pump head is compatible with the valves on your tyres. There are two common types: schrader (like a car tyre valve) and presta (thinner, with a knurled nut on a threaded stalk). All track pumps and most portable pumps will fit both types, using either a reversible pump head (that you take apart and refit) or dual pump heads.
Here's a selection of pumps for use at home and on the bike (both at home and on the bike).
Topeak Turbo Morph with gauge
Topeak were the first to shrink a floor pump to a size that would fit on a bike. They now make several. The Turbo Morph could be your only pump: it has a fold-out pressure gauge, and the foot support, hose, and folding T-handle allow comfortable, high-pressure pumping. It converts between presta and schrader valves. There are cheaper alternatives without the gauge. Weight: 280g. Max pressure: 160psi.
Lezyne Micro Floor Pump HPG
Like Topeak's Turbo Morph, this mini floor pump has a pressure gauge so could be the only one you need. It's available without the gauge for a bit less, and in a high volume (HV) version for quicker fat-tyre inflation as well as this high pressure option. It's made from aluminium, with a fold out foot support and a long hose that connects to presta and schrader valves. There's a mount to fix it to your bike frame too. Weight: 194g. Max pressure: 160psi.
Zefal HPX Vintage Silver
Not many bikes come with the pump pegs you need to clip a long frame-fit pump like this to your bike – which is a shame, as the classic HPX is much easier to use than most mini pumps. It's one of the few non-floor pumps with which it's easy to exceed 100psi. The shortest of the four sizes is 43.5cm long, so is small enough for a courier bag or big pannier. The pump head is reversible to fit schrader or presta valves.
A favourite of cycle workshops, the Rennkompressor is a durable pump that will last decades. If a moving part wears, you can replace it; it's completely rebuildable. The tall pump barrel and shaft are steel, while the handle is wood. It's available with two different pump heads: a classic metal head with an insert for presta valves: and a new EVA head that does either valve. Max pressure: 230psi!
Airace Infinity Sport Steel Floor Pump
This is a good value, steel-barrelled floor pump that easily outperforms chainstore cheapies made of plastic. The pump head fits both presta and schrader valves, automatically adjusting to fit either. It has a pressure gauge, of course, and an air bleeder valve lets you fine tune tyre pressures to within 2 or 3psi. Max pressure: 160psi.
Axiom Propelair G160 Floor Pump
Similar to the Airace above, this is an entry-level floor pump with all the features you really need. It's sturdy, thanks to steel barrel and pump shaft, and very stable thanks to its wide base – so you won't keep knocking it over. The Headrush pump head automatically fits both schrader and presta valves. Max pressure: 160psi.
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