Force and Friction Calculator
Resolve two forces into a resultant, or check whether a block can stay at rest on an incline. Inspect components, friction limits and acceleration after slipping begins.
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Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
For a resultant, add horizontal and vertical force components, then recover magnitude and direction. For an initially stationary block, compare the force needed to hold it with the maximum static friction. If static friction is insufficient, use kinetic friction opposite the initial slipping direction and apply F=ma.
Rx=ΣF cosθ; Ry=ΣF sinθ; R=√(Rx²+Ry²). N=mg cosα; |fs|≤μsN; |fk|=μkN
Worked example
3 N along +x and 4 N along +y combine to 5 N at about 53.13°. A 10 kg block on a 30° incline with g=9.8 has N≈84.87 N and downhill gravity 49 N. With μs=0.6 and no pull, available static friction≈50.92 N is sufficient, so actual friction is 49 N upslope.
Assumptions and input details
Angles increase counterclockwise from +x. A zero resultant has no unique direction. The incline model starts at rest, uses a pull parallel to the surface, and keeps contact with it. Positive force and acceleration point upslope. Enter 0≤μk≤μs≤100 and 0≤incline≤89.999°. It does not describe an already moving block, rolling, variable friction, structural strength or load ratings. Forces, mass and pull are capped at 1e12 in N or kg; g is positive and at most 1000 m/s².
References: OpenStax static and kinetic friction
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
The 19 mass definitions distinguish avoirdupois and troy measures, metric and regional measures. Japanese kin is 600 g; mainland Chinese shijin is 500 g.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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