The ramp length you need, and whether you’ll drag your belly getting up it.

Ramp loading reference: length by height and angle, safe angle bands, breakover lookup

Getting a vehicle up a ramp cleanly comes down to two separate numbers: the angle the ramp sits at, and the angle at which the vehicle’s own belly touches down. The first is set by deck height and ramp length; the second by ground clearance and wheelbase. Both are closed-form, so the values are worth having on hand rather than solving one at a time:

Ramp length   L = H / sin(α)          H = deck height, α = loading angle
Ramp angle    α = arcsin(H / L)        reverse-solve a ramp you already own
Breakover     β = 2 · arctan(2G / WB)  G = ground clearance, WB = wheelbase
Verdict       clears when ramp angle α is below breakover angle β

Ramp length by deck height and loading angle

Minimum straight-ramp length to hold a given angle, in feet and inches. Read across from your measured deck or tailgate height to the angle you want; anything shorter than that cell puts you steeper than the column.

The same slope gets written three ways. A ramp spec printed as "1:12" or "20% grade" is just an angle in disguise:

Heights you are loading over

The deck height is the input every calculation starts from, so measure it rather than guess. Typical ranges for the surfaces people load onto:

Load-type angle bands and what limits each

The safe angle is set by whatever hangs lowest on the load, not by the vehicle’s weight. A riding mower tolerates a steeper climb than a lowered coupe because nothing juts out ahead of its front wheels.

Breakover angle by ground clearance and wheelbase

The angle at which a vehicle high-centers on the transition. If a cell here is lower than your ramp’s angle, that vehicle drags before the ramp’s length ever saves it.

Longer wheelbases and lower clearances both push the breakover angle down, which is why a low car with a long floor pan is the hardest thing to load without scraping.

Related concepts

• Approach and departure angle (SAE J689): the two siblings of breakover. They govern the front and rear overhang clearing a ramp’s lip, where breakover governs the belly at the middle.
• The 1:12 rule: a 4.8° slope from the ANSI A117.1 accessibility standard, written for wheelchairs. Most vendor ramp calculators inherit it, which is why they suggest ramps far longer than a mower or ATV needs.
• Transition and lip radius: real ramps curve at the hinge where they meet the ground. A rounded lip clears slightly better than the sharp geometric corner the breakover formula assumes, so treat a close pass as a fail.
• Rise, run, and grade: three names for one slope. Rise over run is the ratio, rise divided by ramp length gives the sine, and grade is the tangent as a percent.
• Dual ramps: the length and angle math is per ramp and identical whether you run one ramp or a pair, since each wheel track climbs its own incline.