Calculadora de Plano Inclinado
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
a = g·(sinθ−μcosθ)
About this calculator
This calculator determines the acceleration of an object sliding down an inclined plane, considering friction between surfaces. The calculation uses the formula a = g·(sinθ − μ·cosθ), where g is the acceleration due to gravity (9.8 m/s²), θ is the angle of inclination relative to the horizontal, and μ is the coefficient of kinetic friction between the object and the plane. The formula considers that the net force along the plane is the parallel component of weight minus the friction force.
To use the tool, enter the inclination angle in degrees and the friction coefficient (value between 0 and 1). The calculator returns acceleration in m/s². If the value is positive, the object accelerates downwards; if zero, it moves at constant speed; if negative, the object does not slide (friction exceeds the weight component). This is useful for predicting motion in scenarios like ramps, slides, or inclined planes in physics experiments.
Common use cases include: checking whether a block slides or remains stationary on a ramp, determining maximum angles to prevent sliding in engineering projects, and calculating acceleration of objects on inclined planes for kinematics problems. Note that the friction coefficient depends on the materials in contact, and typical values can be found in reference tables.
Cautions: the angle must be in degrees (the calculator automatically converts to radians). The friction coefficient must be between 0 and 1; values outside this range are not physical. The formula assumes a rigid plane and no other forces besides gravity and friction. For static friction problems, use the static friction coefficient, but this formula is for motion (kinetic friction).
Frequently asked questions
What does a negative acceleration result mean?
A negative result indicates that the friction force is greater than the weight component along the plane, so the object does not slide; it remains stationary or would require an extra force to move.
What is the difference between static and kinetic friction in this calculator?
This calculator uses the coefficient of kinetic friction, which applies when the object is moving. To check if the object starts moving, use the static friction coefficient, which is usually larger.
Can I use angles greater than 90 degrees?
No, the angle must be between 0 and 90 degrees, as inclined planes are defined with inclinations from 0° (horizontal) to 90° (vertical).
How do I find the friction coefficient for my materials?
Consult tables of typical friction coefficients for material pairs, such as steel on steel or rubber on concrete. They range from about 0.1 to 0.8.
Does the calculator consider the object's mass?
No, the acceleration on an inclined plane with friction is independent of mass because both friction and the weight component are proportional to mass, which cancels out in the equation.