Use this flywheel torque calculator to solve torque, mass, radius, or angular acceleration for a uniform solid-disk flywheel with built-in unit conversion and instant moment of inertia.
Assumptions & Formulas
– Moment of Inertia (I): I = 0.5 × Mass × Radius²
– Flywheel Torque (τ): τ = Moment of Inertia (I) × Angular Acceleration (α)
Physical Rules:
– Angular acceleration can be negative (indicating deceleration or slowing down). This results in a negative braking torque.
– The physical directions of Torque and Angular Acceleration must match. If estimating Mass or Radius, Torque and Acceleration must have the same mathematical sign.
Note: This calculation assumes the flywheel is a uniform solid disk or cylinder. Results are mathematically rounded to 4 decimal places.
This flywheel torque calculator solves the solid-disk flywheel relationship using the actual mathematical logic behind rotational dynamics. Depending on your needs, the tool can calculate flywheel torque, flywheel mass, flywheel radius, or angular acceleration using the core formula $T = I \times \alpha$ and $I = 0.5 \times m \times r^2$.
We designed this tool to support multiple practical unit paths directly. You can enter mass in kg or lb, radius in m, cm, mm, in, or ft, torque in N·m, lb-ft, or kgf·m, and angular acceleration in rad/s² only. The key assumption to note immediately is that the calculator treats the flywheel as a uniform solid disk or solid cylinder, which matches the standard approach for this specific calculation.
Flywheel Torque Formula
The math behind this calculator relies on the direct relationship between rotational force and a solid object’s resistance to angular acceleration.
Torque from mass, radius, and angular acceleration
The primary calculation relies on Newton’s second law for rotation, linking torque to the moment of inertia and angular acceleration:$$T = I \times \alpha$$
To find the moment of inertia for a uniform solid disk, the tool uses:$$I = 0.5 \times m \times r^2$$
Combining these gives the full formula used to determine torque directly from the physical dimensions and acceleration:$$T = 0.5 \times m \times r^2 \times \alpha$$
Rearranged formulas used by this calculator
When you change the calculation goal, the tool automatically rearranges the core formula to isolate the target variable. The underlying logic uses these specific variations:$$m = \frac{2T}{r^2 \times \alpha}$$$$r = \sqrt{\frac{2T}{m \times \alpha}}$$$$\alpha = \frac{T}{I}$$
What This Calculator Solves
The tool features four distinct calculation modes. Depending on the mode you select, it requires specific inputs and provides a primary result alongside the moment of inertia.
| Calculation goal | Inputs required | Output shown |
|---|---|---|
| Calculate flywheel torque | Mass, radius, angular acceleration | Flywheel torque, moment of inertia |
| Calculate mass of flywheel | Torque, radius, angular acceleration | Mass of flywheel, moment of inertia |
| Calculate radius of flywheel | Torque, mass, angular acceleration | Radius of flywheel, moment of inertia |
| Calculate angular acceleration | Torque, mass, radius | Angular acceleration, moment of inertia |
Inputs and Units Supported by This Tool
The calculator handles unit conversions internally, allowing you to mix and match standard metric and imperial measurements.
| Field | Supported units in the tool |
|---|---|
| Flywheel torque | N·m, lb-ft, kgf·m |
| Mass of the flywheel | kg, lb |
| Radius of the flywheel | m, cm, mm, in, ft |
| Angular acceleration | rad/s² |
| Moment of inertia output | kg·m² |
Unit Conversions Built Into the Calculator
To make calculations faster, this tool automatically handles unit matching behind the scenes. You can input values in your preferred units without manually converting them first.
Torque conversions
The tool seamlessly translates between torque measurements so you do not have to perform manual conversions before entering data:
- N·m ↔ lb-ft
- N·m ↔ kgf·m
Mass conversions
You can input or view the mass result in either metric or imperial units:
- kg ↔ lb
Radius conversions
The calculator accepts multiple length units for the radius, converting them to standard metric internally for the math to work:
- m ↔ cm
- m ↔ mm
- m ↔ in
- m ↔ ft
Moment of Inertia Used in This Flywheel Calculator
Moment of inertia is a measure of how difficult it is to change the object’s rotation speed, and it forms the core of the math used in this tool.
Uniform solid disk assumption
The calculator uses the formula $I = 0.5mr^2$ to determine the moment of inertia. This equation strictly applies to a solid disk or solid cylinder where the mass is distributed uniformly throughout the object. This is the standard baseline used for sizing simple flywheels.
Why moment of inertia is shown with every result
You will notice the moment of inertia appears as a secondary output regardless of the calculation goal you choose. The tool provides this because inertia is the direct intermediate value required to link torque and angular acceleration. It also serves as a highly useful reference metric when you are trying to properly size the mass or radius of a new flywheel design.
Sign Rules for Torque and Angular Acceleration
The calculator supports directional physics, meaning positive and negative signs matter depending on what you are trying to solve.
Negative angular acceleration
The tool accepts negative values for angular acceleration. A negative input simply represents deceleration or a braking force acting on the flywheel rather than speeding it up.
When torque and acceleration must have the same sign
If you are solving for the mass or the radius of the flywheel, the calculator requires the torque and the angular acceleration to share the same directional sign. Both must be positive, or both must be negative, as a physical object cannot have a negative mass or radius.
Input Limits and Calculation Restrictions
The calculator includes safety checks to prevent impossible math or physically invalid scenarios based on the input values.
Values that must be greater than zero
To maintain mathematical validity, the tool enforces specific rules based on real-world physics:
- Mass must be greater than zero when used as an input.
- Radius must be greater than zero when used as an input.
Invalid or indeterminate cases handled by the tool
The calculator includes built-in logic to prevent false or impossible answers:
- Mass or radius cannot be solved when torque is 0 and angular acceleration is 0. This creates an indeterminate state where multiple values could satisfy the equation.
- Mass or radius cannot be solved when angular acceleration is 0 and torque is non-zero, as this would require dividing by zero.
- Radius cannot be solved if the square-root term becomes negative due to mismatched directional signs between torque and acceleration.
How to Use This Flywheel Torque Calculator
Select your goal from the main menu and enter the required values. The tool processes the math instantly based on your selection.
To calculate flywheel torque
- Select Calculate Flywheel Torque from the primary dropdown.
- Enter the mass of the flywheel.
- Enter the radius of the flywheel.
- Enter the angular acceleration.
- Read the resulting flywheel torque and moment of inertia.
To calculate flywheel mass
- Select Calculate Mass of Flywheel.
- Enter the applied torque.
- Enter the radius of the flywheel.
- Enter the angular acceleration.
- Read the required mass and the moment of inertia.
To calculate flywheel radius
- Select Calculate Radius of Flywheel.
- Enter the applied torque.
- Enter the mass of the flywheel.
- Enter the angular acceleration.
- Read the required radius and the moment of inertia.
To calculate angular acceleration
- Select Calculate Angular Acceleration.
- Enter the applied torque.
- Enter the mass of the flywheel.
- Enter the radius of the flywheel.
- Read the resulting angular acceleration and the moment of inertia.
Use Cases for This Calculator
This tool is useful for mechanical sizing and predicting rotational behavior across several common scenarios.
Estimate torque needed to spin up a flywheel
Engineers and hobbyists use this mode to figure out how much motor torque is required to bring a uniform disk up to speed within a specific timeframe.
Back-calculate flywheel mass from required torque
If you have a motor with a known torque output and a desired acceleration profile, you can use the tool to find the exact mass your solid flywheel needs to be.
Size flywheel radius from torque and acceleration targets
When space constraints are flexible but weight and motor power are fixed, this calculation helps determine how wide the disk should be to achieve the desired rotational dynamics.
Find angular acceleration from a known flywheel and applied torque
This is useful for predicting how quickly a specific, existing flywheel will speed up or slow down when a given rotational force is applied to it.
Assumptions and Limitations
Before using the results for engineering applications, it is important to understand the physical boundaries of this specific calculation.
Assumptions
- The calculation assumes the flywheel is a perfectly uniform solid disk or cylinder.
- Angular acceleration must be entered directly in rad/s².
- The torque calculated is the purely inertial torque required for acceleration, not drivetrain-loss corrected engine torque.
Limitations
- The tool does not model ring-shaped flywheels, flywheels with spokes, or custom inertia profiles with uneven mass distribution.
- It does not currently support inputting acceleration in deg/s².
- It does not calculate stored rotational energy, absolute RPM, or required power.
- It does not estimate crank torque from measured wheel torque and drivetrain loss, which involves a completely different mechanical calculation.
FAQ
What formula does this flywheel torque calculator use?
It uses $T = I \times \alpha$ with $I = 0.5 \times m \times r^2$ , so the full flywheel torque formula is $T = 0.5 \times m \times r^2 \times \alpha$ for a uniform solid-disk flywheel.
Can this calculator solve for flywheel mass, radius, or angular acceleration too?
Yes. This tool can solve for torque, mass, radius, or angular acceleration, depending on which calculation goal you select in the menu.
What units does this flywheel torque calculator support?
The tool supports kg and lb for mass, m, cm, mm, in, and ft for radius, N·m, lb-ft, and kgf·m for torque, and rad/s² for angular acceleration.
Why does the calculator show moment of inertia?
Moment of inertia is part of the actual math used to solve the result. The calculator displays it because torque and angular acceleration are directly linked through the relationship $T = I \times \alpha$.
Can flywheel torque be negative?
Yes. In this tool, negative torque or negative angular acceleration represents braking or deceleration, as long as the calculation mode and sign rules are mathematically valid.
Why can’t I solve mass or radius when torque and angular acceleration are both zero?
Because that case is indeterminate for this formula. Multiple mass or radius values could satisfy an equation where both forces are zero, so the tool correctly blocks it instead of returning a false single answer.
Does this calculator work for any flywheel shape?
No. It is explicitly built for a uniform solid disk or cylinder. If your flywheel has a different mass distribution, the inertia formula changes and this specific calculator will not be exact.
Is this the same as converting wheel torque to flywheel torque?
No. That is a different calculation intent based on drivetrain loss and measured wheel torque on a vehicle. This tool calculates inertial flywheel torque directly from mass, radius, and angular acceleration.
Related Tools & Calculators: