Inclined Plane Calculator
Find the acceleration and the parallel, normal, and friction forces acting on a mass resting on a sloped ramp.
kg
°
m/s²
Positive means it slides down the slope
- 1
Parallel (driving) force
5 × 9.81 × sin 30° = 24.525 - 2
Normal force
5 × 9.81 × cos 30° = 42.479 - 3
Friction force
0.2 × 42.479 = 8.496f = μ × N, capped at the driving force - 4
Net force along incline
24.525 − 8.496 = 16.029 - 5
Acceleration
16.029 ÷ 5 = 3.206
How does this calculator work?
On a ramp at angle θ, gravity splits into a parallel pull m·g·sinθ and a normal press m·g·cosθ. Friction μ·m·g·cosθ opposes sliding, so net acceleration is a = g(sinθ − μ·cosθ). Mass cancels out; the block only slides when sinθ exceeds μ·cosθ.
Formula
How this is calculated
Enter the mass m (kg), the incline angle θ in degrees, the coefficient of friction μ (use 0 for frictionless), and gravitational acceleration g (default 9.81 m/s² on Earth). The angle is converted to radians internally.
Gravity is split into two components relative to the ramp surface. The component pulling the mass down the slope is the parallel (driving) force F∥ = m·g·sinθ, while the component pressing into the surface is the normal force N = m·g·cosθ. Friction acts along the surface opposing motion with magnitude f = μ·N, capped at the driving force so a stationary block does not accelerate backward. The net force is F∥ − f, and acceleration is a = net/m = g(sinθ − μ·cosθ).
Assumptions: a rigid, flat ramp, a point mass, a single friction coefficient (kinetic ≈ static here), and motion considered down the slope. Edge cases: at θ = 0 the parallel force and acceleration are zero; at θ = 90° the block is in free fall with N = 0; if μ·cosθ ≥ sinθ the block does not slide and acceleration is zero.
Frequently asked questions
When friction is strong enough (μ·cosθ ≥ sinθ), the friction force fully balances the gravity component along the ramp, so the block stays put and net acceleration is zero.
No. Mass cancels out: a = g(sinθ − μ·cosθ). Heavier objects feel more driving force but also more friction, so the slide acceleration depends only on angle, μ, and g.
Use 9.81 m/s² near Earth's surface. Use 1.62 for the Moon or 3.71 for Mars to model other gravitational fields.
Also known as
TG we-Calculate Editorial Team. (2026). Inclined Plane Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/inclined-plane-calculator
TG we-Calculate Editorial Team. "Inclined Plane Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/inclined-plane-calculator.
TG we-Calculate Editorial Team, "Inclined Plane Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/inclined-plane-calculator
@misc{wecalculate_inclined_plane_calculator, title = {Inclined Plane Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/inclined-plane-calculator}}, year = {2026}, note = {TG we-Calculate} }
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