How this calculation works
Moving cargo changes how two axle supports share its mass even when the cargo weight itself stays fixed. Taking moments about the front support determines the rear reaction. The front reaction then follows from the total vertical force balance.
Rear reaction change = cargo mass × position/wheelbase; front reaction change = cargo mass − rear changeA worked example
A one-tonne load at three metres on a four-metre wheelbase adds 750 kg-equivalent at the rear and 250 at the front. With empty readings of 2000 and 3000 kg, the loaded reactions become 2250 and 3750 kg-equivalent. Moving that same load to five metres adds 1250 at the rear and subtracts 250 from the front. The loaded total remains six tonnes, but its distribution changes substantially.
Good to know
Level-ground rigid-body statics with exactly two axle supports; no suspension, tandem groups, fifth-wheel or dynamic transfer model. This is an educational mass-and-moment calculation, not a roadworthiness, stability, braking, restraint or legal loading approval. Verify actual axle scales and applicable official requirements.
Reference: OpenStax — equilibrium of forces and torques (opens in a new tab) ↗
What this model answers
Moving cargo changes how two axle supports share its mass even when the cargo weight itself stays fixed. Taking moments about the front support determines the rear reaction. The front reaction then follows from the total vertical force balance.
Outputs use kilogram-equivalent reactions because vehicle scale readings are commonly discussed in kilograms. The underlying forces would multiply every mass-equivalent value by gravitational acceleration; the same factor cancels from the reaction split.
The Pallet carton layer layout calculator determines a geometric carton arrangement and gross pallet mass. An axle calculation additionally needs the position of that complete load on the vehicle; carton count alone does not supply its center of mass.
Measure the right inputs
Start with measured empty front and rear axle readings for the actual vehicle condition. Enter cargo position from the front axle along the same horizontal axis as the wheelbase. A load’s position is its center of mass, not necessarily its front edge.
Limits are values you supply. The calculator does not infer legal limits from a vehicle registration, tyre rating or jurisdiction. Gross headroom is checked separately because two individually acceptable axle reactions do not establish every operating constraint.
Read the result in context
Inside the wheelbase, positive cargo mass increases both support reactions. Behind the rear axle it increases rear reaction by more than its own mass and unloads the front support. A negative calculated reaction signals that the assumed two-support static configuration cannot hold.
Summing the reaction changes gives the sum of cargo masses, which is a useful independent check on the table. Position changes redistribute that total; they should not create or remove mass. The signed headroom metrics preserve overloads rather than clipping them to zero.
Work through the numbers
A one-tonne load at three metres on a four-metre wheelbase adds 750 kg-equivalent at the rear and 250 at the front. With empty readings of 2000 and 3000 kg, the loaded reactions become 2250 and 3750 kg-equivalent.
Moving that same load to five metres adds 1250 at the rear and subtracts 250 from the front. The loaded total remains six tonnes, but its distribution changes substantially.
Where the model stops
Level-ground rigid-body statics with exactly two axle supports; no suspension, tandem groups, fifth-wheel or dynamic transfer model.
This is an educational mass-and-moment calculation, not a roadworthiness, stability, braking, restraint or legal loading approval. Verify actual axle scales and applicable official requirements.
A few questions, answered
Why can cargo unload the front axle?
Cargo behind the rear support produces an opposing moment around it; the front reaction falls to maintain static moment balance.
Does gross mass alone prove the load is acceptable?
No. Axle loads, vehicle ratings, restraint and legal operating requirements remain separate checks.