Spring Rate vs Load: Reading a Load-Deflection Curve
Short answer: Spring rate is the slope of the load-deflection curve — how much force changes per unit of travel, in N/mm or lbf/in. Load is a single point on that curve — the force at one specific deflection. A spring rated at 5 N/mm carries 50 N at 10 mm and 100 N at 20 mm; the rate stays constant, the load does not. Buyers who confuse the two usually over-specify travel or under-specify solid height. For a linear compression spring, read rate from the slope and load from the y-value at your working height. BQUQ quotes custom springs in 12 working hours.
Why the Two Terms Get Confused
In everyday purchasing language, "spring load" and "spring rate" are used almost interchangeably. A drawing might say "load 25 N" without stating at what height. A supplier might quote "rate 3 N/mm" without a free length. Neither number means anything on its own.
The confusion is understandable because both are read off the same graph. A load-deflection curve plots force on the vertical axis and deflection (or compressed length) on the horizontal axis. The slope of that line is the rate. Any point on that line is a load. They describe the same spring from two different angles: one is a sensitivity, the other is an operating condition.
For engineers specifying a spring, the practical consequence is this: rate is a design output that follows from wire diameter, coil diameter, active coils, and material modulus. Load is a performance requirement that follows from what the spring must do in the assembly. You specify the load requirement, and the spring design delivers a rate that satisfies it.
The Load-Deflection Curve, Read Properly
A standard linear compression spring produces a straight line from free length down to solid height. Three numbers define it:
- Free length (Lf) — the unloaded length, where load = 0.
- Rate (k) — the slope, in N/mm or lbf/in.
- Solid height (Ls) — the fully compressed length where coils touch.
Load at any deflection is simply:
```
F = k × (Lf − L)
```
where L is the current compressed length. This is Hooke's Law applied to a coil spring, and it holds well within the elastic range.
Where the Line Stops Being Straight
Real curves deviate from the ideal straight line in predictable places:
1. Near solid height. As coils approach contact, the effective number of active coils drops and the curve turns sharply upward. Never design a working point close to solid height unless you intend a progressive rate.
2. At initial tension (extension springs). An extension spring with initial tension holds its coils together until a threshold force is exceeded. The curve starts at zero deflection but non-zero load, then becomes linear.
3. With large deflection. If stress approaches the material's elastic limit, the line bends and the spring takes a permanent set.
4. With tapered or variable-pitch designs. These are deliberately non-linear and cannot be described by a single rate.
For a linear spring, the useful working range is typically between 15% and 85% of available travel. Below that, you waste the spring's capacity; above it, you risk set and fatigue.
Rate vs Load: A Side-by-Side Comparison
| Property | Spring Rate (k) | Spring Load (F) |
|---|---|---|
| What it describes | Slope of the curve | A point on the curve |
| Units | N/mm, lbf/in, kg/mm | N, lbf, kgf |
| Depends on | Wire dia, coil dia, active coils, modulus | Rate × deflection |
| Changes with travel? | No (linear spring) | Yes, proportionally |
| Set by | Spring geometry and material | Assembly working height |
| Typical drawing callout | "Rate 4.2 N/mm" | "Load 30 N at 22 mm" |
| Failure if misread | Wrong stiffness, poor feel | Wrong preload, coil bind |
The table makes the relationship clear: rate is a property, load is a condition. A single spring has exactly one rate (if linear) but infinitely many loads.
How Rate Is Calculated
For a round-wire helical compression spring, the rate follows:
```
k = (G × d⁴) / (8 × D³ × Na)
```
Where:
- G = shear modulus of the material (≈79,000 N/mm² for music wire, ≈69,000 N/mm² for stainless)
- d = wire diameter
- D = mean coil diameter
- Na = number of active coils
The fourth-power dependence on wire diameter is the single most important fact in spring design. Doubling wire diameter multiplies rate by sixteen. That is why small changes in wire gauge produce dramatic stiffness changes, and why spring suppliers hold wire diameter to tight tolerances.
Worked Example
A compression spring with d = 1.2 mm, D = 10 mm, Na = 8, in music wire (G = 79,000 N/mm²):
```
k = (79,000 × 1.2⁴) / (8 × 10³ × 8)
k = (79,000 × 2.0736) / 6400
k ≈ 25.6 N/mm
```
At 5 mm deflection, load ≈ 128 N. At 10 mm, load ≈ 256 N. Same spring, same rate, different loads.
Note that this is an ideal calculation. Real springs show a few percent variation from manufacturing tolerance, which is why spring load testing matters on critical assemblies.
Reading a Curve for Extension and Torsion Springs
The same logic applies, but the axes and intercepts shift.
Extension Springs
An extension spring's curve is offset by initial tension — the internal force holding coils closed. The load equation becomes:
```
F = Fi + k × deflection
```
where Fi is initial tension. On the graph, the line does not pass through the origin; it intercepts the load axis at Fi. Buyers frequently miss this and wonder why a spring reads 8 N before it has moved at all. Our guide to spring initial tension covers how to specify it without over-stressing the hook ends.
Torsion Springs
Torsion springs trade linear force for torque. The curve plots torque (N·mm) against angular deflection (degrees). The slope is the rate in N·mm/degree, and the working point is the torque at a specific rotation angle. The same rate-versus-load distinction applies — just with rotational units.
| Spring Type | Y-axis | X-axis | Slope is called | Intercept |
|---|---|---|---|---|
| Compression | Force (N) | Deflection (mm) | Rate (N/mm) | Zero |
| Extension | Force (N) | Deflection (mm) | Rate (N/mm) | Initial tension Fi |
| Torsion | Torque (N·mm) | Angle (°) | Rate (N·mm/°) | Zero (or leg preload) |
What This Means for Your Specification
When you send a spring requirement to a manufacturer, the most useful package contains:
1. The working load at a stated height or deflection — this is the primary requirement.
2. The available space envelope — free length, max OD, min ID.
3. The travel range — how far the spring moves in service.
4. The environment — temperature, corrosion exposure, cycle count.
Rate is then a derived value, and the spring manufacturer selects wire diameter and coil count to hit your load target within the envelope. If you specify rate alone, you leave the working load undefined and risk a spring that is technically correct but functionally wrong.
A common failure mode: a designer specifies "rate 2 N/mm, free length 40 mm" for a valve that must hold 30 N closed. The spring is made, and at the required 15 mm installed height it delivers exactly 30 N — but only if the tolerance stack holds. Adding a load-at-height callout with a tolerance band removes the ambiguity. For more on how geometry drives stress and rate together, see spring index and stress.
Tolerances That Matter
| Parameter | Typical commercial tolerance | Precision tolerance |
|---|---|---|
| Wire diameter | ±0.02 mm | ±0.01 mm |
| Free length | ±1.5% | ±0.5% |
| Rate | ±10% | ±5% |
| Load at height | ±10% | ±5% |
| Squareness | 3° | 1.5° |
These are indicative figures, not guarantees. Rate tolerance is especially sensitive to active coil count — a single extra coil changes rate by roughly 1/Na.
Non-Linear Curves: When One Rate Is Not Enough
Some applications deliberately want a curve that bends. Three common approaches:
- Variable pitch — coils spaced unevenly so they close progressively, raising rate as travel increases.
- Conical or tapered springs — rate rises as coils of decreasing diameter become active.
- Belleville and wave washers — very high rate over a short deflection, often stacked to tune the curve.
If your requirement reads "soft at first, stiff at the end," you are asking for a non-linear curve, and you should say so explicitly rather than quoting a single rate. Our comparison of wave vs Belleville springs covers when each profile wins.
Manufacturing Reality: Why Curves Shift
Two springs made to the same drawing can produce slightly different curves. The main causes:
- Wire diameter variation — amplified by the fourth power.
- Coil count — off-by-one errors change rate noticeably.
- Heat treatment and stress relief — affects the modulus slightly and the set behavior significantly.
- End condition — closed and ground ends behave differently from closed-not-ground.
This is why reputable spring manufacturers test a sample from each lot and report load at the specified height, not just rate. At BQUQ, springs are produced across four production lines in one Dongguan factory under ISO9001, with wire forming, coiling, and heat treatment controlled in-house. CNC machining holds ±0.005 mm where spring seats and mating hardware need it.
Frequently Asked Questions
Q: Is spring rate the same as spring constant?
A: Yes, in practice. "Spring constant" and "spring rate" both refer to the slope of the load-deflection curve, usually denoted k. The term "constant" emphasizes that the value does not change with deflection for a linear spring. For non-linear springs, engineers prefer "rate" because the value does vary across the travel range.
Q: Can two springs have the same rate but different loads?
A: Absolutely. Rate depends only on geometry and material; load depends on how far the spring is compressed. A 5 N/mm spring at 10 mm gives 50 N, while another 5 N/mm spring at 30 mm gives 150 N. If your assembly has a fixed working height, you must specify load at that height, not rate alone.
Q: How do I convert spring rate from N/mm to lbf/in?
A: Multiply N/mm by 5.7101. A rate of 4 N/mm equals roughly 22.8 lbf/in. To go the other way, multiply lbf/in by 0.1751. Always confirm which unit system your supplier uses, because a misread conversion on a stiff spring can put the design well outside its intended working range.
Q: What happens if I compress a spring past its rated deflection?
A: Beyond the recommended deflection, stress approaches the material's elastic limit. The spring may take a permanent set, meaning it will not return to free length. Compressing to solid height repeatedly accelerates fatigue and can crack the wire. Design working travel to stay within roughly 85% of available deflection.
Q: Does temperature change spring rate?
A: Yes, modestly. Shear modulus drops as temperature rises, so rate falls slightly. For music wire and stainless steels, the change is small within normal industrial ranges but becomes significant above roughly 150 °C. At high temperature, consider alloy steels or Inconel and confirm the modulus at your operating temperature.
Related Resources
- About BQUQ and our Dongguan manufacturing footprint: /about/
- Custom compression springs: /compression-springs/
- Custom extension springs: /extension-custom-springs/
- Custom torsion springs: /torsion-springs/
- Industry trends in spring and metal component sourcing: /industry-dynamics/
- Technical articles and engineering guides: /bquq-blog/
- Frequently asked questions: /faq/
- Contact our engineering team: /contact/
Authored by the BQUQ Engineering Team. BQUQ (Dongguan) runs CNC machining (±0.005 mm), metal stamping, custom springs, and heat sink production in one ISO9001 factory. Source-direct from Dongguan, China — quote in 12 hours: sc@bquq.com | WhatsApp +86 13713157787 | www.bquq.com
