Hand Truck Balance and Handle Force Calculator

A sack truck is a lever with a bad reputation. Everyone knows to tilt it back and almost nobody knows there is one tilt angle at which the load balances over the axle and the handles carry nothing at all — and that past that angle the handles carry more, not less. With a 180 lb load sitting 18 in up the frame and 6 in out from it, that balance point is 18 degrees from vertical. At 25 degrees the handles are holding 19 lb. At 45 degrees they are holding 45 lb, a quarter of the load, and the operator is doing it with their back.

Treated as sitting over the axle, so it goes to the wheels and not to the handles.
Measured along the frame. For a stack of even boxes it is roughly the toe plate height plus half the stack height.
Half the depth of the load if it sits flat against the frame. A drum, a water heater or an appliance on a strap can be a lot more, and this is the number that sets where the balance point falls.
Zero is the frame standing straight up. Measured from vertical, not from the ground and not from the ramp.
Rise over run times 100. Set it to zero for a flat floor.
Pneumatic tyres on smooth concrete are low, hard wheels on rough or soft ground are several times that. Pull the loaded truck along a flat floor with a fish scale and divide by the weight, and you have your own figure instead of anybody else's.
Hand Truck Balance Calculator — Handle and Wheel LoadBuildFigure

There is a tilt angle where the handles carry nothing

A loaded hand truck balances when the centre of gravity of the load passes directly over the axle. Two dimensions decide where that happens: how far the load centre sits up the frame from the axle, and how far it stands out from the frame. The balance tilt is the arctangent of the second divided by the first — with the default 6 in out and 18 in up, that is 18.4 degrees back from vertical.

Below that angle the load is still ahead of the axle and it is trying to fall away from the operator, so the handles are pulled upward. Above it the load has passed behind the axle and the handles are pressing down. The page reports which side of the balance point you are on and in which direction, because a negative number here is a change of direction rather than a small force.

More tilt is more handle force, not less

This is the part that runs against instinct. Once past the balance angle, every extra degree of tilt-back increases what the handles carry, and it does so all the way. The single exception is a load sitting flat against the frame with no standoff at all, where the force is the same at every angle and equal to the ceiling below. The handle force is the load times the quantity (frame distance minus the standoff times the cotangent of the tilt), divided by the handle distance — and the cotangent shrinks as the angle grows, so the force only ever climbs.

With the defaults, 25 degrees gives 19.2 lb at the handles, 45 degrees gives 45.0 lb — a quarter of the 180 lb load — and the value tends toward a ceiling of 67.5 lb as the frame goes flat. That ceiling is the load times the up-the-frame distance over the handle distance, and it is the most the handles can ever carry for that geometry no matter how far the truck is laid over.

Longer handles, or a load that sits lower

Two of the four dimensions are things you can actually change. A longer handle distance divides the force down directly: the same load with hands 60 in from the axle rather than 48 puts 15.4 lb on them at 25 degrees rather than 19.3. Stacking a load so its centre of gravity is lower on the frame does the same thing, and it lowers the ceiling as well.

The standoff works the other way, and it is the one people control least. A drum, a water heater or a safe strapped to the frame puts the load centre a long way out, drives the balance angle up, and makes the truck fight to stand back up until you have tilted well past it.

The ramp is a separate force in a separate direction

The push needed to move the whole thing up an incline is the gross weight times the sine of the ramp angle plus the rolling resistance times its cosine. On the defaults — 202 lb gross, 8 percent grade, 0.06 coefficient — that is 28.2 lb along the ramp. It sits on the operator at the same time as the vertical handle force, and it is a completely different number in a completely different direction.

It also assumes a steady walk. Starting from a stop is more, and holding it back on the way down is the same force pointed the other way with nothing but the operator to supply it.

Questions people ask

At what angle does a hand truck balance?

At the arctangent of how far the load centre of gravity stands out from the frame divided by how far it sits up the frame from the axle. With the page defaults, 6 in out and 18 in up, that is 18.4 degrees back from vertical. At exactly that tilt the load is over the axle and the handles carry nothing at all.

Does tilting a hand truck further back make it lighter to hold?

No — it makes it heavier, and this is the thing most people have backwards. Past the balance angle every extra degree of tilt puts more on the handles, and it never puts less. With the defaults it is 19 lb at 25 degrees and 45 lb at 45 degrees, and it climbs toward a ceiling of 67.5 lb as the frame goes flat.

Why do the handles sometimes want to lift up?

Because you are tilted back less than the balance angle, so the load is still ahead of the axle and gravity is standing the truck up rather than laying it down. The page reports that as an upward force at the handles rather than a negative number, because it is a change of direction. It is also the direction in which a load comes off the toe plate.

How do I reduce the force on my hands?

Get the load centre of gravity lower on the frame, get it closer in to the frame, or use a truck with longer handles. The force is proportional to the up-the-frame distance and inversely proportional to the handle distance, so hands at 60 in instead of 48 in cut the default 19.2 lb to 15.4 lb with nothing else changed.

How much force does it take to push a hand truck up a ramp?

Gross weight times the sine of the ramp angle, plus rolling resistance times its cosine. With the defaults — 202 lb gross on an 8 percent grade at a 0.06 coefficient — that is 28.2 lb along the ramp. It is separate from and additional to the vertical force at the handles, and it assumes a steady walk rather than a start from a stop.

Where do I get the rolling resistance number?

From your own wheels on your own floor. Pull the loaded truck along a flat surface with a fish scale, divide the reading by the gross weight, and that is the coefficient. Pneumatic tyres on smooth concrete are low and hard wheels on rough or soft ground are several times higher, and a measured figure beats any number copied from somewhere else.

Related