Calculate the uphill force needed to move an object up an incline at constant speed using mass, angle, and friction, with results in N or lbf.
Customize This Calculator
Build your own version. Describe what you want changed, added, or compared.
- All Physics Calculators
- All Force Calculators
- Upward Force Calculator
- Lateral Force Calculator
- Incline Plane Force Calculator
Uphill Force Formula
The uphill force is the force needed to move an object up an incline at constant speed while overcoming gravity and friction. The calculator uses this formula:
- F = uphill force, in newtons (N)
- m = mass of the object, in kilograms (kg)
- g = acceleration due to gravity, 9.81 m/s²
- a = incline angle, in radians
- mu = coefficient of friction
The first part of the formula, m*g*sin(a), is the component of the object’s weight pulling it back down the slope. The second part, mu*m*g*cos(a), is the friction force that also resists uphill motion.
If you enter mass in pounds, the calculator converts it to kilograms before applying the formula. If you enter the angle in degrees, it converts the angle to radians for the sine and cosine calculations. The result is calculated in newtons, then converted to pounds-force if you choose lbf as the output unit.
Common Coefficients of Friction
The coefficient of friction depends on the two surfaces in contact. Use the table as a rough reference when an exact value is not given.
| Surface Pair | Typical Coefficient of Friction | Notes |
|---|---|---|
| Rubber on dry concrete | 0.6 to 1.0 | High traction |
| Rubber on wet concrete | 0.3 to 0.7 | Lower traction than dry concrete |
| Wood on wood | 0.2 to 0.5 | Varies with surface finish |
| Steel on steel | 0.1 to 0.2 | Low friction, especially if smooth |
| Ice on ice | 0.02 to 0.1 | Very low friction |
Incline Angle Reference
| Incline Angle | Radians | General Meaning |
|---|---|---|
| 5° | 0.0873 | Very gentle slope |
| 10° | 0.1745 | Moderate ramp |
| 20° | 0.3491 | Steep incline |
| 30° | 0.5236 | Very steep incline |
| 45° | 0.7854 | Extremely steep slope |
Example Calculations
Example 1: Force in newtons
Find the uphill force for a 50 kg object on a 20° incline with a coefficient of friction of 0.30.
Using 20° = 0.3491 radians:
The required uphill force is about 306.01 N.
Example 2: Force with pounds-force output
Find the uphill force for a 100 lb object on a 15° incline with a coefficient of friction of 0.20.
First convert mass to kilograms:
Apply the uphill force formula:
Convert newtons to pounds-force:
The required uphill force is about 45.18 lbf.
FAQ
What does uphill force mean?
Uphill force is the force applied parallel to an incline to move an object up the slope. In this calculator, the result assumes the object moves at constant speed, so the applied force balances the downhill component of gravity and friction.
Why does friction increase the required uphill force?
Friction acts opposite the direction of motion. If the object is moving uphill, friction acts downhill along the slope. That means you need extra force to overcome both gravity and friction.
What happens if the coefficient of friction is zero?
If the coefficient of friction is zero, the friction part of the formula becomes zero. The uphill force is then only the force needed to overcome the downhill component of gravity:
