Calculate the pulling force needed to drag a load on level ground or up an incline with friction, or solve for the mass or acceleration from a known pull.

0° is level ground.

Typical kinetic (sliding) friction values; real surfaces vary with finish, moisture and load.

0 means a steady pull at constant speed; negative means slowing while moving upward.

Optional settings

Arithmetic comparison only; this does not select safe or rated lifting equipment. Blank uses 1.

Pull Force Formula

The following equation is used to calculate the required pull force to move an object up an incline with friction (pulling parallel to the slope).

Fₚ = m(a + gsin(θ) + μ gcos(θ))
  • Where Fp is the required pull force along the incline (N)
  • m is the mass of the object (kg)
  • a is the acceleration along the incline (m/s2)
  • g is gravitational acceleration (≈ 9.81 m/s2)
  • θ is the incline angle measured from horizontal
  • μ is the coefficient of friction (unitless; typically kinetic friction for a moving object)

This parallel-pull formula assumes the object is already sliding up the incline and kinetic friction acts down the plane. At constant speed, a = 0. For pull angle α above the plane, the calculator uses F = m[a + g(sinθ + μcosθ)] / (cosα + μsinα), with normal force N = mgcosθ − Fsinα. A negative tensile pull or negative normal force is outside this model. Negative acceleration means slowing while still moving upward; stopping or reversing requires a new friction analysis. See OpenStax’s friction model. The optional multiplier is arithmetic and does not establish a safe equipment rating.

What is a Pull Force?

Definition:

A pull force is an applied force that pulls on an object. The object’s acceleration depends on the net force (the sum of all forces), so the applied pull force is not always equal to ma when other forces (such as gravity and friction) are present.

How to Calculate Pull Force?

Example Problem:

The following example outlines the steps and information needed to calculate the pull force up an incline with friction.

First, determine the mass of the object. In this example, the mass of the object is 5 kg.

Next, determine the incline angle and coefficient of friction. For this example, the incline angle is 20° and the coefficient of friction is 0.20.

Then determine the desired acceleration along the incline. In this example, the object accelerates up the slope at 3 m/s2.

Finally, calculate the pull force using the formula above:

Fp = m(a + gsin(θ) + μgcos(θ))

For a pull parallel to the plane (α = 0°), using g = 9.80665 m/s²: Fp = 5(3 + 9.80665sin(20°) + 0.20·9.80665cos(20°)).

Fp ≈ 5(3 + 3.35407 + 1.84305).

Fp ≈ 40.9856 N ≈ 41.0 N.