Inputs
Example data table
| Length (m) | Rise (m) | Angle (°) | Coeff | Mass (kg) | IMA | Normal (N) | Friction (N) | Effort (N) | Pred. MA | Eff. (%) |
|---|---|---|---|---|---|---|---|---|---|---|
| 5.00 | 1.00 | 11.54 | 0.100 | 120 | 5.000 | 1,153.0 | 115.3 | 350.7 | 3.356 | 67.1 |
| 4.00 | 0.80 | 11.54 | 0.200 | 75 | 5.000 | 720.6 | 144.1 | 291.2 | 2.526 | 50.5 |
| 6.00 | 1.50 | 14.48 | 0.050 | 200 | 4.000 | 1,899.0 | 95.0 | 585.3 | 3.351 | 83.8 |
| 3.50 | 0.70 | 11.54 | 0.150 | 90 | 5.000 | 864.8 | 129.7 | 306.2 | 2.882 | 57.6 |
| 8.00 | 1.00 | 7.18 | 0.000 | 150 | 8.000 | 1,459.5 | 0.0 | 183.9 | 8.000 | 100.0 |
Values assume steady motion and pulling parallel to the ramp.
Formula used
- Angle: θ = arcsin(rise ÷ length) (when angle is not entered).
- Ideal MA: IMA = length ÷ rise = 1 ÷ sin(θ).
- Weight: W = m·g (when mass is entered).
- Components: W∥ = W·sin(θ), N = W·cos(θ).
- Friction: Ff = coefficient · N.
- Effort: F = W·sin(θ) + coefficient·W·cos(θ).
- Actual MA: AMA = W ÷ effort (when effort is entered).
- Efficiency: η = (AMA ÷ IMA) × 100.
How to use this calculator
- Select units for length, mass, and force.
- Enter ramp geometry using angle or length and rise.
- Choose sliding or rolling friction, then enter a coefficient.
- Pick a gravity preset, or enter a custom value.
- Provide the load as mass or weight, then calculate.
- Optionally add applied effort to get actual advantage.
- Optionally add travel and time for work and power.
Inclined plane mechanical advantage guide
1) Geometry sets ideal advantage
An inclined plane trades distance for force. If the slope length is 6 m and the rise is 1 m, the ideal mechanical advantage is L/H = 6. Without friction, you need about one‑sixth of the load’s weight along the ramp. Steeper ramps shrink IMA quickly and increase required effort.
2) Angle and grade interpretation
Angles are useful for design checks. A 1:4 slope (25% grade) is about 14.0°, while a 1:12 access ramp (8.3% grade) is about 4.8°. For any angle θ, IMA equals 1/sin(θ). Small angles raise IMA, but the ramp becomes longer and needs more floor space. The run is √(L²−H²) for simple layouts.
3) Friction reduces real performance
Friction adds an extra term μ·cos(θ) to the required effort. On gentle slopes, cos(θ) is near 1, so friction can dominate. With θ ≈ 10° and μ = 0.20, μ·cos(θ) ≈ 0.197, often larger than sin(10°) ≈ 0.174. If you are unsure, start with μ between 0.05 and 0.30 and refine from a test push. Smooth plastics may be near the low end; rough rubber can be higher.
4) Estimating effort with numbers
Suppose a 100 kg load has weight W ≈ 981 N. On a 5 m ramp with 1 m rise, sin(θ)=0.20 and cos(θ)≈0.98. Effort without friction is W·sin(θ) ≈ 196 N. With μ=0.10, effort becomes W·(0.20 + 0.10·0.98) ≈ 292 N (about 66 lbf).
5) Actual vs predicted advantage
If you enter a measured effort, the calculator reports actual mechanical advantage (AMA = W/Effort). You can compare that to the predicted advantage using the friction model. The efficiency shown is (AMA/IMA)×100%, a quick way to see losses and compare surface choices. This also helps validate vendor ramp ratings.
6) Rolling resistance option
Some wheels behave more like rolling resistance than sliding friction. Using a small coefficient Crr (often 0.01–0.05 for many hard wheel setups) can better match carts and dollies. The coefficient represents rolling losses and bearing drag, so real values change with wheel size and surface. Even small Crr values add up over distance.
7) Practical design checks
Use the output to sanity‑check safety and workflow. Verify the required effort is below what your team, winch, or motor can provide continuously. If efficiency drops below about 50%, improving the surface, adding rollers, or reducing angle can cut effort and stabilize motion. For holding a load at rest, add a safety margin or a brake. Remember: lower effort usually means longer travel distance.
FAQs
What is the difference between IMA and AMA?
IMA comes from geometry only (L/H or 1/sinθ). AMA uses your measured effort: W divided by effort. AMA is usually smaller because friction and deformation waste energy, especially on rough or dirty ramps.
Should I enter angle or length and rise?
Either works. Angle is convenient when a ramp is already specified. Length and rise are useful when you are measuring a real setup. If you provide both, the calculator prioritizes the angle and still estimates length and rise if possible.
What friction coefficient should I use?
Use a value that matches your surface and motion. If unsure, start with 0.10 for smoother sliding, 0.20 for average rough contact, and adjust after a test push. Rolling setups usually use smaller coefficients such as 0.01–0.05.
Why does efficiency drop on gentle slopes?
On shallow angles, sinθ is small, so the gravity component along the ramp is small. Friction depends on cosθ, which stays near 1, so friction becomes a larger share of the required effort and efficiency falls.
Can the calculator estimate power?
Yes, if you enter travel distance and time. Power is work input divided by time. This helps size motors and winches for continuous duty. For short bursts, consider peak loads and safety factors.
Do the results include acceleration or starting force?
No. The equations assume steady motion at constant speed. Starting from rest may require more force due to static friction, bumps, or wheel binding. Add margin and use chocks, a brake, or a spotter when safety matters.