**Wheel torque** can be calculated function of **engine torque** if the parameters and status of the transmission are known. In this tutorial, we are going to calculate the wheel torque and force for a given:

- engine torque
- gear ratio (of the engaged gear)
- final drive ratio (at the differential)
- (free static) wheel radius

Also, we are going to assume that there is **no slip** in the clutch or torque converter, the engine being mechanically linked to the wheels.

This method can be applied to any powertrain architecture (front-wheel drive or rear-wheel drive) but, for an easier understanding of the components, we are going to use a **read-wheel drive (RWD) powertrain**.

Image: Vehicle rear-wheel drive (RWD) powertrain diagram

As depicted in the image above, the engine is the source of torque. The gearbox is connected to the engine through the clutch (on a manual transmissions) or torque converter (on an automatic transmissions). We consider that there is absolutely no slip in the clutch (fully closed) or in the torque converter (lock-up clutch closed). In this case the engine torque *T _{e} [Nm]* is equal with the clutch/torque converter torque

*T*.

_{c}[Nm]\[T_c = T_e \tag{1}\]

Further, the **engine torque** is transmitted through the gearbox, where is multiplied with the gear ratio of the engaged gear *i _{x} [-]* and outputs the

**gearbox torque**

*T*.

_{g}[Nm]\[T_g = i_x \cdot T_e \tag{2}\]

The propeller shaft is transmitting the torque to the rear axle, where is multiplied with the final drive gear ratio *i _{0} [-]*. This gives the

**torque at the differential**

*T*.

_{d}[Nm]\[T_d = i_0 \cdot T_g \tag{3}\]

If the vehicle is driven on a straight line, the torque at the differential is equally split between the left wheel *T _{lw} [Nm]* and the right wheel

*T*.

_{rw}[Nm]\[T_{lw} = T_{rw} = \frac{T_d}{2} \tag{4}\]

Image: Vehicle rear-wheel drive (RWD) powertrain schematic

The sum of the left and right wheel torque gives the **torque at the differential**.

\[T_{lw} + T_{rw} =T_d \tag{5}\]

Replacing (2) in (3) in (4) gives the **mathematical expression of the wheel torque function of the engine torque**, for a given gearbox ratio *i _{x}* and a final drive ratio

*i*.

_{0}\[\bbox[#FFFF9D]{T_w = \frac{i_x \cdot i_0 \cdot T_e}{2} }\tag{6}\]

If we consider n_{w} [-] as the number of driving wheels, then the wheel torque formula will have the general form of:

\[\bbox[#FFFF9D]{T_w = \frac{i_x \cdot i_0 \cdot T_e}{n_{w}} }\tag{6.1}\]

If the vehicle is rear wheel drive (RWD) or front wheel drive (FWD) then n_{w} = 2, if the vehicle is four wheel drive (4WD) or all wheel drive (AWD) the n_{w} = 4. If the vehicle is a motorcycle then n_{w} = 1.

The **formula of the wheel torque** (6) applies to a vehicle which is driven on a straight line, where the left wheel torque is equal with the right wheel torque.

\[T_{lw} = T_{rw} = T_w \tag{7}\]

From mechanics (static), we know that the **torque** is the product between a **force** and its **lever arm length**. In our case, the wheel torque is applied in the wheel hub (center) and the lever arm is the wheel radius *r _{w} [m]*. For this example we assume that both wheel have the same radius

*r*.

_{w}\[T_{lw} = F_{lw} \cdot r_w \tag{8}\]

The same principle applies to the **right wheel torque**.

\[T_{rw} = F_{rw} \cdot r_w \tag{9}\]

Assuming that both left and right wheel torque and radius are equal, we can write a generic expression of the wheel force *F _{w} [N]*, function of wheel torque

*T*and wheel radius

_{w}[Nm]*r*.

_{w}[m]\[T_{w} = F_{w} \cdot r_w \tag{10}\]

From (10) we can extract the formula of the **wheel force** function of the **wheel torque** and **wheel radius**.

\[\bbox[#FFFF9D]{F_{w} = \frac{T_w}{r_w}} \tag{11}\]

Replacing (6) in (10) will give the mathematical expression of the **wheel force** function of **engine torque**, gearbox **gear ratio**, **final drive ratio** and **wheel radius**.

\[\bbox[#FFFF9D]{F_{w} = \frac{i_x \cdot i_0 \cdot T_e}{2 \cdot r_w}} \tag{12}\]

For a different number of driving wheels n_{w} [-], the **general formula for wheel force** becomes:

\[\bbox[#FFFF9D]{F_{w} = \frac{i_x \cdot i_0 \cdot T_e}{n_{w} \cdot r_w}} \tag{12.1}\]

**Example 1**. Calculate the **wheel torque** and **force** for a rear wheel drive vehicle (RWD) with the following parameters:

- engine torque, T
_{e}= 150 Nm - gearbox (1
^{st}) gear ratio, i_{x}= 4.171 - final drive ratio, i
_{0}= 3.460 - tire size marking 225/55R17

**Step 1**. Calculate the (free static) **wheel radius** from the tire size marking. The method for calculating the wheel radius is described in the article How to calculate wheel radius. The calculated wheel radius is r_{w} = 0.33965 m.

**Step 2**. Calculate the **wheel torque** using equation (6).

\[T_w = \frac{i_x \cdot i_0 \cdot T_e}{2} = \frac{4.171 \cdot 3.460 \cdot 150}{2} = 1082.3745 \text{ Nm}\]

**Step 3**. Calculate the **wheel force** using equation (11).

\[F_{w} = \frac{T_w}{r_w} = \frac{1082.3745}{0.33965} = 3186.7349 \text{ N} \]

**Example 2**. For a given gearbox, with multiple gears (gear ratios), we can calculate the **wheel torque** and **force** for each gear. Let’s calculate the **wheel torque** and force for a vehicle with the following parameters:

- engine torque, T
_{e}= 150 Nm - wheel radius, r
_{w}= 0.33965 m

The gearbox is automatic (ZF6HP26), with the following gear ratios and final drive ratio.

Gear # | Gear ratio symbol | Gear ratio |

1 | i_{1} | 4.171 |

2 | i_{2} | 2.340 |

3 | i_{3} | 1.521 |

4 | i_{4} | 1.143 |

5 | i_{5} | 0.867 |

6 | i_{6} | 0.691 |

Final drive | i_{0} | 3.460 |

To speed up calculations, we can use a Scilab script.

clc// Input dataTe = 150;ix = [4.171 2.340 1.521 1.143 0.867 0.691];i0 = 3.460;rw = 0.33965;nw = 2;// Wheel torque and force calculationTw = (ix .* i0 .* Te)/nw;Fw = Tw ./ rw;// Display resultsmprintf("\n%s\t\t%s\t\t%s\t\t%s\n","Gear","ix [-]","Tw [Nm]","Fw [N]")for i=1:length(ix) mprintf("%d\t\t%.3f\t\t%.2f\t\t%.2f\n",i,ix(i),Tw(i),Fw(i));end

Executing the above script will output the following results in the Scilab console:

Gearix [-]Tw [Nm]Fw [N]14.1711082.373186.7322.340607.231787.8131.521394.701162.0841.143296.61873.2850.867224.99662.4160.691179.31527.94

**Example 3**. For our third example we are going to use the full load torque curve of an engine and calculate the **wheel torque and force** (traction) in each gear. Calculate the wheel torque and force (traction) for a vehicle with the following parameters:

- engine torque, T
_{e}= 150 Nm - wheel radius, r
_{w}= 0.33965 m - the gear ratios of ZF6HP26 (see
**Example 2**)

The engine torque at full load is given by the following parameters:

N_{e} [rpm] | 800 | 1312 | 1800 | 2276 | 2800 | 3316 | 3806 | 4300 | 4770 | 5300 | 5800 | 6300 |

T_{e} [Nm] | 116 | 135 | 148 | 157 | 165 | 172 | 178 | 184 | 188 | 187 | 183 | 171 |

where N_{e} is **engine speed** and T_{e} is **engine torque**.

The graphical representation of the engine speed and torque points is depicted in the image below.

Image: Engine torque at full load function of engine speed

Since we need to perform a lot of calculations, we’ll use a Scilab script to calculate the **wheel torque** and force curves for each gear. The results are going to be plotted in a graphical window.

clc// Input dataNe = [800 1312 1800 2276 2800 3316 3806 4300 4770 5300 5800 6300];Te = [116 135 148 157 165 172 178 184 188 187 183 171];ix = [4.171 2.340 1.521 1.143 0.867 0.691];i0 = 3.460;rw = 0.33965;nw = 2;// Plot engine torquefigure(1)hf = gcf();hf.background = 8;plot(Ne,Te,"LineWidth",2)xgrid()xlabel("Engine speed [rpm]","FontSize",3)ylabel("Engine torque [Nm]","FontSize",3)title("x-engineer.org","Color","blue","FontSize",2)// Calculate wheel torque and forcefor i = 1:length(ix) for j = 1:length(Te) Tw(i,j) = (ix(i) .* i0 .* Te(j))/nw; Fw(i,j) = Tw(i,j) ./ rw; endend// Plot wheel torque and forcefigure(2)hf = gcf();hf.background = 8;plot(Ne,Tw,"LineWidth",2)xgrid()xlabel("Engine speed [rpm]","FontSize",3)ylabel("Wheel torque [Nm]","FontSize",3)title("x-engineer.org","Color","blue","FontSize",2)legend("1st gear","2nd gear","3rd gear","4th gear","5th gear","6th gear",2)figure(3)hf = gcf();hf.background = 8;plot(Ne,Fw,"LineWidth",2)xgrid()xlabel("Engine speed [rpm]","FontSize",3)ylabel("Wheel force [N]","FontSize",3)title("x-engineer.org","Color","blue","FontSize",2)legend("1st gear","2nd gear","3rd gear","4th gear","5th gear","6th gear",2)

Executing the script will output the following graphical windows.

Image: Wheel torque at full load function of engine speed and gear

Image: Wheel force at full load function of engine speed and gear

The same method can be applied for an **electric vehicle**, the engine torque being replaced by the **motor torque**.

You can also check your results using the calculator below.

### Wheel torque calculator

T_{e} [Nm] | i_{x} [-] | i_{0} [-] | r_{w} [m] | n_{w} [-] |

T_{w} [Nm] = | ||||

F_{w} [N] = |

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## FAQs

### How do you calculate wheel torque? ›

To calculate the torque seen at the wheel, **divide the engine torque by the drive train loss ratio**.

**What is the formula to calculate torque? ›**

How is torque calculated? τ = F ⋅ r \tau = F\cdot r τ=F⋅rtau, equals, F, dot, r. The direction of the torque vector is found by convention using the right hand grip rule.

**How do you calculate torque needed to rotate a wheel PDF? ›**

To calculate load torque, **multiply the force (F) by the distance away from the rotational axis, which is the radius of the pulley (r)**. If the mass of the load (blue box) is 20 Newtons, and the radius of the pulley is 5 cm away, then the required torque for the application is 20 N x 0.05 m = 1 Nm.

**How is torque calculated in cars? ›**

The formula for figuring out torque is **torque = horsepower of the engine x 5252, which is then divided by the RPMs**. The problem with torque, however, is that it is measured in two different places: directly from the engine and to the drive wheels.

**What is the formula for a wheel? ›**

Use the formula: **c = 2_pi_r**, where c is the circumference, r is the radius, and pi can be approximated by 3.14. Following the example, if the car wheel has a radius of 0.3 meters, then the circumference is equal to: 0.3 x 3.14 x 2 = 1.89 meters.

**How do you calculate power to wheels? ›**

Now, write power as torque T (Newtons) times angular velocity w (radians per second) where RPM is wheel RPM. P = 2 pi T RPM/60 = mav. That's it. The wheel RPM is directly proportional to velocity, so once you know torque, mass and velocity, you can calculate acceleration.

**Why do we calculate torque? ›**

When studying how objects rotate, it quickly becomes necessary **to figure out how a given force results in a change in the rotational motion**. The tendency of a force to cause or change rotational motion is called torque, and it's one of the most important concepts to understand in resolving rotational motion situations.

**How do you solve torque problems? ›**

How to Solve Torque Problems Easily - YouTube

**How do you calculate torque with hand rule? ›**

The Right Hand Rule for Torque - YouTube

**How do you calculate torque in torsion? ›**

The equivalent torque can be found with: where **n[rad/s] = N[rev/min]×2π/60**. Similar to the moments of inertia that you learned before in rotational kinetics and bending of beams, the polar moment of inertia represents a resistance to twisting deformation in the shaft.

### How do you calculate flywheel torque? ›

**Tfw = m*r^2/2/a**

- Where Tfw is the Flywheel Torque (N-m)
- m is the flywheel mass (kg)
- r is the radius (m)
- a is the angular acceleration (rad/s^2)

**How do you calculate rotating flywheel torque? ›**

In this experiment a flywheel is so mounted that torques can be applied to it by hanging a mass M from the free end of a string, the remainder of which is wrapped around the axle. The torque due to the weight is **τ = Tr where T is the tension in the string and r the radius of the axle**.

**What is torque in engine or car? ›**

Torque is **a twisting force that speaks to the engine's rotational force and measures how much of that twisting force is available when an engine exerts itself**. Torque is present in everyday happenings, such as operating a doorknob, opening a soda bottle, using a wrench, or pedaling a bicycle.

**What is the formula for wheel and axle? ›**

In the case of a wheel and axle, the ideal mechanical advantage can be calculated using the equation **IMA=Rr** I M A = R r where R is the radius of the wheel and r is the radius of the axle.

**How do you calculate wheel HP? ›**

The equation to calculate horsepower is simple: **Horsepower = Torque x RPM / 5,252**.

**How is wheel size calculated? ›**

Wheel Diameter

Wheel or rim diameter is **the distance measured in inches across the face of the wheel, from bead seat to bead seat**. It's measured this way because that's where the tire and the wheel come together. In our example, the diameter is 16 inches.

**How much power do you lose from engine to wheels? ›**

Broadly, **15 per cent of the engine's peak power** is lost to friction, getting to to the wheels from the crank. So 300 kilowatts/horsepower (whatever) at the crank is about 250 at the wheels (ballpark estimate). But manufacturers all measure power at the crank.

**How much torque does a 1 HP motor have? ›**

The 3600 RPM, 1HP motor produces **1.5 ft.** **lbs.** of torque at 3600 RPM. So if your 1HP pump was operating at 1800 RPM, the 1800 RPM motor would be producing 3 ft.

**How do you calculate engine force? ›**

The force (thrust) is equal to **the exit mass flow rate times the exit velocity minus the free stream mass flow rate times the free stream velocity**.

**What are the 3 factors that determine torque? ›**

Examples: Page 5 Torque is Determined by Three Factors: **The magnitude of the applied force.** **The direction of the applied force.** **The location of the applied force**.

### What is the unit of torque? ›

The SI unit for torque is the **Newton-metre or kgm ^{2}sec-^{2}**. How have we come to this? If we look at the formula Torque = Force X Distance. While distance is measured in metres and force is measured in newton, so torque is measured in newton ⋅ metres.

**Does torque change with speed? ›**

Since the rated output power of a motor is a fixed value, **speed and torque are inversely related**. As output speed increases, the available output torque decreases proportionately.

**What is torque formula and examples? ›**

Solved Example on Torque Formula

The distance from the bolt to the mechanic's hand is 0.40 m. Find out the magnitude of the torque applied? Answer: The angle between the moment the arm of the wrench and the force is without a doubt 90°, and sin 90° θ = 1. The torque is: **T = F × r × sinθ**

**How do you find torque from distance? ›**

Ch 15 Torque Fundamentals (5 of 13) How to Calculate a ... - YouTube

**How do you calculate torque in fluid mechanics? ›**

Physics - Mechanics: Fluid Statics (1 of 1) Calculating the Torque on a ...

**Is torsion equal to torque? ›**

Torque and torsion are both related to turning effects experienced by a body. The main difference between torque and torsion is that torque describes something that is capable of producing an angular acceleration, whereas **torsion describes the twist formed in a body due to a torque**.

**What is the formula of torsion constant? ›**

From its definition, we see that the torsion constant may be obtained by plotting a graph of torque vs. angular displacement and calculating the slope. **Κ = I 2Tπ** . The STATIC METHOD and DYNAMIC METHOD can be performed in either order, but you must use the same rod in both parts of the experiment.

**What is the formula for torsional stiffness? ›**

where **I _{p} = π D ^{4}/32** is the polar moment of inertia of a circular cross section. Thus, the torque required for unit twist, i.e., T (θ) is called the torsional stiffness.

**What is flywheel formula? ›**

Moment of inertia of a flywheel is calculated using the given formula; **I = N m N + n ( 2 g h ω 2 − r 2 )**

**What is the torque for flywheel bolts? ›**

Tighten all bolts evenly, ¼ turn at a time in a crisscross pattern until flywheel is completely drawn-up to the crankshaft. Torque all bolts in 3 steps: First to 25 ft/lbs. then 60 ft/lbs. Final torque to: **78 - 80 ft/lbs**.

### How do you measure a flywheel? ›

Using a dial caliper, measure from the flywheel friction surface to the straight-edge. Record the distance. Again, using the dial caliper, measure from the engine housing flange to the straight-edge. Subtract this distance from the previously recorded distance.

**What is the formula for rotating? ›**

...

Rotation Formula:

Rotation | Point coordinate | Point coordinate after Rotation |
---|---|---|

Rotation of 90^{0} (Anti-Clockwise) | (x, y) | (-y, x) |

Rotation of 180^{0} (Both) | (x, y) | (-x, -y) |

Rotation of 270^{0} (Clockwise) | (x, y) | (-y, x) |

Rotation of 270^{0} (Anti-Clockwise) | (x, y) | (y, -x) |

**How do you calculate counterclockwise torque and clockwise? ›**

Ch 15 Torque Fundamentals (2 of 13) Direction of Torque (Part 1) - YouTube

**How do you calculate net torque in physics? ›**

Physics, Net Torque (5 of 13) Five Forces Applied to a Door - YouTube

**What's the difference between torque and torque? ›**

Horsepower vs Torque - A Simple Explanation - YouTube

**What is engine torque used for? ›**

Applied to internal combustion engines or electric motors, torque **indicates the force to which the drive shaft is subjected**. Torque is expressed in pound-feet (lb-ft) or newton-meters (Nm). The interaction of torque and engine speed (rpm) determines the engine power.

**How do you calculate torque from horsepower? ›**

- Torque (lb.in) = 63,025 x Power (HP) / Speed (RPM)
- Power (HP) = Torque (lb.in) x Speed (RPM) / 63,025.
- Torque (N.m) = 9.5488 x Power (kW) / Speed (RPM)
- Power (kW) = Torque (N.m) x Speed (RPM) / 9.5488.

**What is torque formula and examples? ›**

Solved Example on Torque Formula

The distance from the bolt to the mechanic's hand is 0.40 m. Find out the magnitude of the torque applied? Answer: The angle between the moment the arm of the wrench and the force is without a doubt 90°, and sin 90° θ = 1. The torque is: **T = F × r × sinθ**

**Is torque R * F or F * R? ›**

If F is force and r is radius, then torque =**F ×r**.

**What is the formula of torque in magnetic field? ›**

**τ = N I A B sinθ**

This is the torque on a current-carrying loop in a uniform magnetic field. This equation can be shown to be valid for a loop of any shape. The loop carries a current I, has N turns, each of area A and the perpendicular to the loop makes an angle θ with the field B. The net force on the loop is zero.

### How do you calculate torque in KG? ›

Torque is measured in Newton meters and is calculated by **N·m = (kg*m²)/s²**.

**How do you calculate torque and torque? ›**

Measure the distance, r , between the pivot point and the point the force is applied. Determine the angle θ between the direction of the applied force and the vector between the point the force is applied to the pivot point. **Multiply r by F and sin θ** and you will get the torque.

**What are the 3 units of torque? ›**

Torque Units: SI, Metric and American

There are three common torque units: **SI (International Standard) based on Newton meters, Metric based on kilogram force centimeters, and American/ English based on inch pounds**.

**What are the three types of torque? ›**

In order to ensure proper operation of indicating instruments, the following three torques are required: **Deflecting torque.** **Controlling torque.** **Damping torque**.

**What is torque equal to? ›**

By definition, torque **τ = r × F**. Therefore, torque on a particle is equal to the first derivative of its angular momentum with respect to time.

**What does R stand for in torque? ›**

Equation. Symbol breakdown. Meaning in words. τ = r F sin θ = r ⊥ F \tau = rF\sin\theta = r_\perp F τ=rFsinθ=r⊥F. τ \tau τ is torque, F is applied force, r is the radius from the axis of rotation to the location where the force is exerted, and θ is the angle between F and r when these vectors are placed tail to tail.

**What is torque example? ›**

Torque is **the expression of a rotational or twisting force**. The engines in vehicles rotate about an axis, thus creating torque. It can be viewed as the strength of a vehicle. Torque is what rockets a sports car from 0-60 kmph in seconds.

**What is universal torque equation? ›**

The universal torque equation is obtained when all the elements are considered in the relay i.e., **T = T _{1} + T_{2} + T_{3} + T_{4}**. Substituting equations of T

_{1}, T

_{2}, T

_{3}, and T

_{4}in the above equation, we get, T = K

_{1}I

^{2}+ K

_{2}V

^{2}+ K

_{3}V I cos(θ - 𝜏) + K

_{4}. The above equation represents the universal torque equation of relay.

**How do you calculate torque in a circular coil? ›**

Calculating the Torque on a Current Carrying Coil in a Magnetic Field

**What is the formula for the torque on a current loop? ›**

Torque on the loop can be found using **τ=NIABsinθ** τ = N I A B sin θ . Maximum torque occurs when θ=90∘ θ = 90 ∘ and sinθ=1 sin θ = 1 .