# Safety Margin Versus Safety Factor

## Introduction

This article covers how to calculate safety margins, how to calculate safety factors and the difference between the two. We'll also address how the factor of safety and safety margin are related.

The safety factor can be found by dividing the maximum stress something can sustain without failing by the stress it will generally experience. | Source

## How Do You Determine The Safety Factor?

Safety factor can be found by finding ultimate strength of an item like a bridge and then dividing it by the working stress the bridge would be under. Safety factor can also be found by dividing the yield strength by the allowable or working stress.

Another way of calculating the safety factor is by dividing the maximum safe load just below the load at which the item will fail by the normal safety load it will generally experience. You can also estimate the safety factor by dividing the computed strength of a modeled load, but this value must be mediated by the uncertainties of the design and predicted usage. Safety factor can be found by dividing the fatigue limit to the maximum working stress. This will be the limit at which an object will fail divided by the highest load it will experience.

If a bridge can hold 10,000 tons and it will normally hold 5,000 tons, the safety factor is 10,000 divided by 5,000 or 2.0. If a chair can hold 300 pounds but normally seats people who weigh 200 pounds, the safety factor is 300 divided by 200 or 1.5.
What if you are calculating safety factor by dividing the fatigue limit to the maximum working stress? Using the example of an elevator, you would use the fatigue limit of the elevator cable at 3,000 pounds by the maximum working stress of 1,000 pounds for a safety factor of 3.0, not the average load of 500 pounds, which would give a safety factor of 3000 divided by 500 for 6.0.

Safety factors should never be less than 1.0, since this indicates that it is regularly subjected to its maximum load and almost certain to fail during expected usage. Safety factors of 1.5 or 2.0 suggest that the structure or object can handle its maximum expected load and unusual circumstances such as horrific traffic jams or high winds.
You cannot have a negative safety factor. If a theoretical design has a safety factor that is a fraction or less than one, the design is not safe. If your bridge has an expected yield stress of 500 tons and it is supposed to handle 600 tons of vehicles, the safety factor is 5/6 - and the bridge will probably collapse.

Safety Factor
50 pounds
10 pounds
5.0
5,000 tons
1,000 tons
5.0
500 tons
200 tons
2.5
500 tons
500 tons
1.0

## How Do You Determine The Safety Margin?

The safety margin or margin of safety is related to the safety factor, but they are not the same value. The safety margin is the safety factor minus one.

If a bridge is designed to hold 9,000 tons and regularly holds 3,000, the safety factor is 9,000 divided by 3,000 or 3.0. The safety margin for the bridge is then 3.0 minus one, yielding a safety margin of 2.0. If an elevator is designed to handle a 4 ton load before failing and regularly carries 2 tons, the safety factor is 4 divided by 2 for a safety factor of 2.0. The safety margin is then 2.0 minus 1 or 1.0.

The safety margin is fractional when the safety factor is between 1.0 and 2.0. For example, a safety factor of 1.5 minus one gives a safety margin of 0.5. Ideally, the safety margin is at least 1.0 while the safety factor is at least 2.0. However, increasing the robustness of a design typically increases its cost, if only in the additional materials and labor to make a thicker, heavier, more durable structure.

If the safety margin is one, the safety factor is zero. When the safety factor is zero, the object or design is already subjected to the maximum load it can tolerate - there is no margin for error. A negative margin of safety means the object will fail during expected usage.

Safety Factor
Safety Margin

3 or higher
2 or higher
Acceptable
2
1
Borderline
1
0
Dangerous

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