One of the questions we get asked most often is, "How do I determine
what pump I need?"
This is always a hard question, unless the fountain will be a tabletop
model where little or no lift is required. In this case we can recommend one
of the smaller pumps.
When building taller fountains or built-into-the-wall fountains or
outdoor water features where the actual fountain may need to be higher than
the main pool of water, the formula gets tricky.

Most pumps are rated by "GPH"  or gallons per hour. This is the
maximum amount of water that the pump will put out with no tubing or
attachments to the spout.  As the demand for the pump to lift water
increases ( by adding a few inches or feet of tubing ), the actual GPH of
the pump decreases.

The other term that pump manufacturers use is "max head" or maximum
head or maximum lift. This is the measurement of the maximum height the pump
will lift water before it runs out of pumping power. The actual max head can
be achieved by adding tubing to the pump... but remember, this will decrease
the gph and flow of water.

Most pump companies (including ours) provide tables listing the
various pump models, gph and max head. The tables also list the gallons per
hour the different models will pump at different heights... 6", 1', 2',
etc., so the requirements for a pump can begin to be figured out using these
details.

The pump used should be able to circulate the amount of water in the
container used approximately once per hour. The capacities of most
containers are usually included somewhere on the label when they're
purchased. If the container is not too large, you can measure the capacity a
gallon or 5 gallons at a time by adding water that way.

Once the capacity of the container is determined, the amount of lift
must be taken into consideration. An 80 gph pump will circulate water at 80
gph, in a 24" high 1/2 barrel container that holds 25 gallons of water... if
the pump sits just below the water surface.
But when the pump is dropped to the bottom of the barrel, you've added
2' of lift that the pump has to supply. Add to that a fountain head of any
kind and you will increase the lift by that height. The 80 gph pump with a
max head rating of 22" will be inadequate.

Our personal formula for choosing pumps for our projects goes like
this. We first figure out how much max head ( lift ) we want for a
particular project. In our barrel fountains, we wanted enough head to set
the pumps on the bottom of the barrel. (We later suspended our pumps a few
inches off the bottom so they wouldn't pick up sedement ). We also wanted to
be able to use our decorative hand pumps (14" tall) or our feather rock
waterfalls ( varying heights), or our water faucet feature (14" tall). This
gave us the max head requirement of at least 38". We looked at the table for
our pumps and quickly determined that the 140 gph pump had a max head of 4'
and  would give us 45 gph at at 3'.
We also looked at the 120 gph pump, which had a max head rating of
42", but at 3' the gph was only 10 gph. We decided to go with the larger
pump and have the option of adjusting the flow pump
down to where we wanted it.

The 140 gph pump provided us with the lift ( max head) we needed, the
gph to circulate the water in the container once per hour and still left us
with adjustment to control the flow of water. We didn't want it gushing, so
we adjusted the pump down until the water ran gently from our fountain
feature.

Now, there are probably more scientific ways of determining pump
requirements for your project, but this is how we do it.  :)

Note: Using a fountain accent, fountain stone or fountain head with a
waterway that has a smaller diameter than the pump spout or tubing will
greatly decrease the amount of water getting to the top of the accent.

Also, when shopping for a pump, make sure that if you need the pump to
be adjustable, it is adjustable within the range you need. Many pumps do not
adjust from 0 flow, but start the from mid range to maximum flow. This will
prevent you from slowing the water down to a trickle even though your pump
may only be rated at 60 gallons per hour.