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# Friction - Friction Coefficients and Calculator

The friction force is the force exerted by a surface when an object moves across it - or makes an effort to move across it.

The frictional force can be expressed as

Ff = μ N                     (1)

where

Ff = frictional force (N, lb)

μ = static (μs) or kinetic (μk) frictional coefficient

N = normal force between the surfaces (N, lb)

There are at least two types of friction forces

• kinetic (sliding) friction force- when an object moves
• static friction force - when an object makes an effort to move

For an object pulled or pushed horizontally the normal force - N - is simply the gravity force - or weight:

N = Fg

= m ag                         (2)

where

Fg = gravity force - or weight (N, lb)

m = mass of object (kg, slugs)

ag = acceleration of gravity (9.81 m/s2, 32 ft/s2)

The friction force due to gravity (1) can with (2) be modified to

Ff = μ m ag                      (3)

### Friction Coefficients for some Common Materials and Materials Combinations

Friction Coefficients vs. Materials and Surface Conditions
Materials and Material CombinationsSurface Conditions, LubricantFrictional Coefficient
Static
- μstatic -
Kinetic (sliding)
- μsliding -
Aluminum Aluminum Clean and Dry 1.05 - 1.35 1.4
Aluminum Aluminum Lubricated and Greasy 0.3
Aluminum-bronze Steel Clean and Dry 0.45
Aluminum Mild Steel Clean and Dry 0.61 0.47
Aluminum Snow Wet 0oC 0.4
Aluminum Snow Dry 0oC 0.35
Brake material2) Cast iron Clean and Dry 0.4
Brake material2) Cast iron (wet) Clean and Dry 0.2
Brass Steel Clean and Dry 0.51 0.44
Brass Steel Grease 0.19
Brass Steel Castor oil 0.11
Brass Cast Iron Clean and Dry 0.3
Brass Ice Clean 0oC 0.02
Brass Ice Clean -80oC 0.15
Brick Wood Clean and Dry 0.6
Bronze Steel Grease 0.16
Bronze Cast Iron Clean and Dry 0.22
Bronze - sintered Steel Grease 0.13
Cadmium Chromium Clean and Dry 0.41
Cadmium Mild Steel Clean and Dry 0.46
Cast Iron Cast Iron Clean and Dry 1.1 0.15
Cast Iron Cast Iron Clean and Dry 0.15
Cast Iron Cast Iron Grease 0.07
Cast Iron Oak Clean and Dry 0.49
Cast Iron Oak Grease 0.075
Cast iron Steel Clean and Dry 0.4
Cast iron Steel Clean and Dry 0.23
Cast iron Steel Grease 0.21 0.133
Car tire Asphalt Clean and Dry 0.72
Car tire Grass Clean and Dry 0.35
Carbon (hard) Carbon Clean and Dry 0.16
Carbon (hard) Carbon Grease 0.12 - 0.14
Carbon Steel Clean and Dry 0.14
Carbon Steel Grease 0.11 - 0.14
Chromium Chromium Clean and Dry 0.41
Chromium Chromium Grease 0.34
Copper-Lead alloy Steel Clean and Dry 0.22
Copper Copper Clean and Dry 1.6
Copper Copper Grease 0.08
Copper Cast Iron Clean and Dry 1.05 0.29
Copper Steel Clean and Dry 0.53 0.36
Copper Steel Grease 0.18
Copper Steel Oleic acid 0.18
Copper Glass Clean and Dry 0.68 0.53
Diamond Diamond Clean and Dry 0.1
Diamond Diamond Grease 0.05 - 0.1
Diamond Metals Clean and Dry 0.1 - 0.15
Diamond Metal Grease 0.1
Garnet Steel Clean and Dry 0.39
Glass Glass Clean and Dry 0.9 - 1.0 0.4
Glass Glass Grease 0.1 - 0.6 0.09 - 0.12
Glass Metal Clean and Dry 0.5 - 0.7
Glass Metal Grease 0.2 - 0.3
Glass Nickel Clean and Dry 0.78
Glass Nickel Grease 0.56
Graphite Steel Clean and Dry 0.1
Graphite Steel Grease 0.1
Graphite Graphite (in vacuum) Clean and Dry 0.5 - 0.8
Graphite Graphite Clean and Dry 0.1
Graphite Graphite Grease 0.1
Hemp rope Timber Clean and Dry 0.5
Horseshoe Rubber Clean and Dry 0.68
Horseshoe Concrete Clean and Dry 0.58
Ice Ice Clean 0oC 0.1 0.02
Ice Ice Clean -12oC 0.3 0.035
Ice Ice Clean -80oC 0.5 0.09
Ice Wood Clean and Dry 0.05
Ice Steel Clean and Dry 0.03
Iron Iron Clean and Dry 1.0
Iron Iron Grease 0.15 - 0.20
Lead Cast Iron Clean and Dry 0.43
Leather Oak Parallel to grain 0.61 0.52
Leather Metal Clean and Dry 0.4
Leather Metal Grease 0.2
Leather Wood Clean and Dry 0.3 - 0.4
Leather Clean Metal Clean and Dry 0.6
Leather Cast Iron Clean and Dry 0.6 0.56
Leather fiber  Cast iron Clean and Dry 0.31
Leather fiber Aluminum Clean and Dry 0.30
Magnesium Magnesium Clean and Dry 0.6
Magnesium Magnesium Grease 0.08
Magnesium Steel Clean and Dry 0.42
Magnesium Cast Iron Clean and Dry 0.25
Masonry Brick Clean and Dry 0.6 - 0.7
Mica Mica Freshly cleaved 1.0
Nickel Nickel Clean and Dry 0.7 - 1.1 0.53
Nickel Nickel Grease 0.28 0.12
Nickel Mild Steel Clean and Dry 0.64
Nickel Mild Steel Grease 0.178
Nylon Nylon Clean and Dry 0.15 - 0.25
Nylon Steel Clean and Dry 0.4
Nylon Snow Wet 0oC 0.4
Nylon Snow Dry -10oC 0.3
Oak Oak (parallel grain) Clean and Dry 0.62 0.48
Oak Oak (cross grain) Clean and Dry 0.54 0.32
Oak Oak (cross grain) Grease 0.072
Paper Cast Iron Clean and Dry 0.20
Phosphor-bronze Steel Clean and Dry 0.35
Platinum Platinum Clean and Dry 1.2
Platinum Platinum Grease 0.25
Plexiglas Plexiglas Clean and Dry 0.8
Plexiglas Plexiglas Grease 0.8
Plexiglas Steel Clean and Dry 0.4 - 0.5
Plexiglas Steel Grease 0.4 - 0.5
Polystyrene Polystyrene Clean and Dry 0.5
Polystyrene Polystyrene Grease 0.5
Polystyrene Steel Clean and Dry 0.3 - 0.35
Polystyrene Steel Grease 0.3 - 0.35
Polyethylene Polytehylene Clean and Dry 0.2
Polyethylene Steel Clean and Dry 0.2
Polyethylene Steel Grease 0.2
Rubber Rubber Clean and Dry 1.16
Rubber Cardboard Clean and Dry 0.5 - 0.8
Rubber Dry Asphalt Clean and Dry 0.9 0.5 - 0.8
Rubber Wet Asphalt Clean and Dry 0.25 - 0.75
Rubber Dry Concrete Clean and Dry 0.6 - 0.85
Rubber Wet Concrete Clean and Dry 0.45 - 0.75
Silk Silk Clean 0.25
Silver Silver Clean and Dry 1.4
Silver Silver Grease 0.55
Sapphire Sapphire Clean and Dry 0.2
Sapphire Sapphire Grease 0.2
Silver Silver Clean and Dry 1.4
Silver Silver Grease 0.55
Skin Metals Clean and Dry 0.8 - 1.0
Steel Steel Clean and Dry 0.5 - 0.8 0.42
Steel Steel Grease 0.16
Steel Steel Castor oil 0.15 0.081
Steel Steel Stearic Acid 0.15
Steel Steel Light mineral oil 0.23
Steel Steel Lard 0.11 0.084
Steel Steel Graphite 0.058
Steel Graphite Clean and Dry 0.21
Straw Fiber Cast Iron Clean and Dry 0.26
Straw Fiber  Aluminum Clean and Dry 0.27
Tarred fiber Cast Iron Clean and Dry 0.15
Tarred fiber Aluminum Clean and Dry 0.18
Polytetrafluoroethylene (PTFE) (Teflon) Polytetrafluoroethylene (PTFE) Clean and Dry 0.04 0.04
Polytetrafluoroethylene (PTFE) Polytetrafluoroethylene (PTFE) Grease 0.04
Polytetrafluoroethylene (PTFE) Steel Clean and Dry 0.05 - 0.2
Polytetrafluoroethylene (PTFE) Snow Wet 0oC 0.05
Polytetrafluoroethylene (PTFE) Snow Dry 0oC 0.02
Tungsten Carbide Steel Clean and Dry 0.4 - 0.6
Tungsten Carbide Steel Grease 0.1 - 0.2
Tungsten Carbide Tungsten Carbide Clean and Dry 0.2 - 0.25
Tungsten Carbide Tungsten Carbide Grease 0.12
Tungsten Carbide Copper Clean and Dry 0.35
Tungsten Carbide Iron Clean and Dry 0.8
Tin Cast Iron Clean and Dry 0.32
Tire, dry Road, dry Clean and Dry 1
Tire, wet Road, wet Clean and Dry 0.2
Wax, ski Snow Wet 0oC 0.1
Wax, ski Snow Dry 0oC 0.04
Wax, ski Snow Dry -10oC 0.2
Wood Clean Wood Clean and Dry 0.25 - 0.5
Wood Wet Wood Clean and Dry 0.2
Wood Clean Metal Clean and Dry 0.2 - 0.6
Wood Wet Metals Clean and Dry 0.2
Wood Stone Clean and Dry 0.2 - 0.4
Wood Concrete Clean and Dry 0.62
Wood Brick Clean and Dry 0.6
Wood - waxed Wet snow Clean and Dry 0.14 0.1
Wood - waxed Dry snow Clean and Dry 0.04
Zinc Cast Iron Clean and Dry 0.85 0.21
Zinc Zinc Clean and Dry 0.6
Zinc Zinc Grease 0.04

Kinetic or sliding frictional coefficient only when there is a relative motion between the surfaces.

Note! It is commonly thought that the static coefficients of friction are higher than the dynamic or kinetic values. This is a very simplistic statement and quite misleading for brake materials. With many brake materials the dynamic coefficient of friction quoted is an "average" value when the material is subject to a range of sliding speeds, surface pressures and most importantly operating temperatures. If the static situation is considered at the same pressure, but at ambient temperature, then the static coefficient of friction is often significantly LOWER than the average quoted dynamic value. It can be as low as 40 - 50% of the quoted dynamic value.

### Kinetic (Sliding) versus Static Frictional Coefficients

Kinetic or sliding frictional coefficients are used with relative motion between objects. Static frictional coefficients are used for objects without relative motion. Note that static coefficients are somewhat higher than the kinetic or sliding coefficients. More force are required to start a motion

### Example - Friction Force

A 100 lb wooden crate is pushed across a concrete floor. The friction coefficient between the object and the surface is 0.62. The friction force can be calculated as

Ff = 0.62 (100 lb)

= 62 (lb)

• 1 lb = 0.4536 kg

### Example - Car, Braking, Friction Force and Required Distance to Stop

A car with mass 2000 kg drives with speed 100 km/h on a wet road with friction coefficient 0.2.

Note! - The friction work required to stop the car is equal to the kinetic energy of the car.

The kinetic energy of the car is

Ekinetic = 1/2 m v2                           (4)

where

Ekinetic = kinetic energy of the moving car (J)

m = mass (kg)

v = velocity (m/s)

Ekinetic = 1/2 (2000 kg) ((100 km/h) (1000 m/km) / (3600 s/h))2

=  771605 J

The friction work (energy) to stop the car can be expressed as

Wfriction = Ff d                                (5)

where

Wfriction = friction work to stop the car (J)

Ff = friction force (N)

d = braking (stopping) distance (m)

Since the kinetic energy of the car is converted to friction energy (work) - we have the expression

Ekinetic = Wfriction                              (6)

The friction force Ff can be calculated from (3)

Ff = μ m g

= 0.2 (2000 kg) (9.81 m/s2)

= 3924 N

The stop distance for the car can be calculated by modifying (5) to

d = Wfriction / Ff

= (771605 J) / (3924 N)

= 197 m

Note! - since the mass of the car is present on both sides of eq. 6 it cancels out. The stop distance is not dependent on the mass of the car.

### "Laws of Friction"

#### Unlubricated Dry Surfaces

1. for low pressure the friction is proportional to the normal force between the surfaces. With rising pressure the friction will not rise proportionally. With extreme pressure friction will rise and surfaces seize.
2. at moderate pressure the friction force - and coefficient - is not dependent of the surface areas in contact as long as the normal force is the same. With extreme pressure friction will rice and surfaces seize.
3. at very low velocity between the surfaces the friction is independent of the velocity of rubbing. With increased velocity the the friction decrease.

#### Lubricated Surfaces

1. friction force is almost independent of pressure - normal force - if the surfaces are flooded with lubricant
2. friction varies with speed at low pressure. At higher pressure the minimum friction is at velocity 2 ft/s (0.7 m/s) and friction increases with approximately square root of velocity afterwards.
3. friction varies with temperature
4. for well lubricated surfaces the friction is almost independent of surface material

Typically steel on steel dry static friction coefficient 0.8 drops to 0.4 when sliding is initiated - and steel on steel lubricated static friction coefficient 0.16 drops to 0.04 when sliding is initiated.

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