Free Engineering Calculator
Disc Spring (Belleville Washer) Calculator
A disc spring (Belleville washer) gives a high force in a small space. Its force at a given deflection depends on the outside and inside diameters, thickness and free height. Enter the dimensions below; the calculator uses the DIN 2092 (Almen-Laszlo) method for a single spring.
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Maximizing Load in Minimal Space
Disc springs, often referred to as Belleville washers, are engineered to handle massive loads within extremely restricted spaces. Unlike traditional coil springs, a disc spring provides a high degree of force with a very small deflection. These components are critical for maintaining bolt preload, absorbing shocks, or acting as thermal expansion compensators in high-pressure joints.
Understanding the force-deflection curve of a single disc is only the beginning. By stacking these springs, you can customize the spring rate and travel distance to meet your specific application requirements. Precise calculation of these stacks ensures your assembly remains stable under varying environmental stresses.
Stacking Logic
Imperial to Metric: 1 Inch = exactly 25.4 mm.
Metric to Imperial: 1 mm = 0.03937 inches.
Interactive Disc Spring Design Tool
Input your disc dimensions and material properties below to calculate spring force at specific deflections. Use this data to determine the ideal stacking configuration for your mechanical assembly.
Disc Spring Calculator
Calculate spring force and technical performance for Belleville washers and disc springs.
Recommended max deflection: 75% of (l0 - t).
Calculated Spring Force (F)
Newtons (N)
Diameter Ratio ($\delta$)
0.00
Inner Height ($h_0$)
0.00
Force in Lbf
0.00
Spring Rate (R)
0.00
Theoretical Spring Work (J, scientific notation)
0.00e+0 J
*Calculations based on the Almen-Laszlo equations as given in DIN 2092 (DIN EN 16984); dimensions to DIN 2093 (DIN EN 16983).
Material: Spring Steel (E = 206,000 MPa, ν = 0.3).
How to Use the Disc Spring Calculator
- Enter the outside diameter De and inside diameter Di in millimeters.
- Enter the material thickness t and the free (unloaded) overall height l0.
- Enter the deflection s you want to check. DIN 2093 (DIN EN 16983) catalog forces are usually quoted at 75% of the free cone height h0 = l0 – t.
- Read the spring force, the ratio De/Di, the cone height and the approximate spring rate.
The Formula and a Worked Example
DIN 2092 gives the force as F = [4E / (1 – µ²)] x [t⁴ / (K1 x De²)] x (s/t) x [(h0/t – s/t)(h0/t – s/2t) + 1], with E = 206,000 MPa and µ = 0.3 for spring steel, and K1 a factor that depends only on De/Di.
Example: DIN 2093 series A, 40 x 20.4 x 2.25 mm with free height 3.15 mm. Cone height h0 = 0.90 mm. At 75% deflection (s = 0.675 mm) the calculator gives about 6,500 N (1,460 lbf).
For stacks, springs nested in parallel multiply the force; springs stacked in series multiply the deflection. Friction between nested springs adds a few percent to the loading force, so check critical stacks with the manufacturer.
Critical Design Factors
| Factor | Engineering Impact | Performance Goal |
|---|---|---|
| Load at Flat | The theoretical maximum force when the disc is compressed fully. | Avoids overstressing. |
| Spring Rate | The amount of force required per unit of deflection. | Ensures consistent tension. |
| Fatigue Life | Determines how many cycles the spring can withstand before failure. | Maximizes longevity. |
| Hysteresis | The friction produced when stacking springs in parallel. | Accounts for damping effects. |
Frequently Asked Questions
What is the difference between a disc spring and a Belleville washer?
They are the same part. Belleville washer is the common US name; disc spring is the name used in DIN 2093 and DIN EN 16983.
How much force does a Belleville washer give?
It depends on size and deflection. A 40 mm series A spring gives about 6,500 N at 75% deflection; a 20 x 10.2 x 1.1 mm spring about 1,500 N.
What is the difference between DIN 2092 and DIN 2093?
DIN 2093 (now DIN EN 16983) sets the standard dimensions and quality of disc springs. DIN 2092 (now DIN EN 16984) gives the calculation method used here.
How do you stack disc springs?
Stacking in the same direction (parallel) multiplies force; alternating direction (series) multiplies deflection. Combinations of both tune force and travel.
Next Steps
- Washers and disc springs: Belleville and spring washers we supply
- Bolt Torque Calculator: the preload a disc spring has to hold
- Ask an engineer: sizing a spring stack
- Request a quote for the fasteners in your joint.
Related Calculators
More free tools for the same job:
- Bolt Size and Strength Calculator: Estimate the bolt size and strength class an application needs.
- Standard Torque and Preload Calculator: Calculate tightening torque and preload for hex and socket head screws.
- Force Converter: Convert force and load between units.
- Torque and Preload with Friction Scatter: Calculate torque and preload across a friction range.
Building a Custom Spring Stack?
Our technical team can help you select materials and stack configurations that offer the highest fatigue life for your specific load environment.