# How to Calculate a Weight-to-Strength Ratio ••• dolgachov/iStock/GettyImages

A low weight-to-strength ratio is not only desirable in the gym. The weight-to-strength ratio, when descriptive of a material, relates the density of the material to its ability to withstand permanent deformation or fracture under pressure. Low-ratio values indicate that the material is light-weight but can bear significant load. High values describe heavy materials that deform or break easily. The weight-to-strength ratio is typically used in an inverse form as the strength-to-weight ratio; it is then termed the specific strength of the material.

Measure the mass of the material using the scale. For example, if you are determining the weigh-to-strength ratio of titanium, weigh the titanium and report the mass in grams (g) or kilograms (kg). To convert the titanium mass from grams to kilograms, divide the mass by 1,000. For example, a mass of 9.014 grams is equivalent to 0.009014 kg: 9.014/1000 = 0.009014.

Determine the volume of the material. For regularly shaped samples, use a ruler to measure the dimensions of the sample and calculate the volume from the dimensions. For example, if the material is in the form of a cube with side lengths of 1 cm, the volume of the cube equals the side-length cubed: 1 x 1 x 1 = 1 cm^3. For irregularly shaped samples, the volume may be obtained by a process of fluid displacement. Measure the water level in a graduated cylinder before and after submerging the sample in the water. The change in water level is equivalent to the volume of the specimen in cubic centimeters. For example, if the water level before adding the sample is 10 cm^3 and the water level after adding the sample is 15 cm^3, the sample volume is five cubic centimeters: 15 - 10 = 5. Convert volumes given in cubic centimeters to cubic meters by dividing by 1 x 10^6. For example, a volume of 5 cm^3 equals 5 x 10^-6 m^3: 5/1 x 10^6 = 5 x 10^-6.

Calculate the density of the material by dividing the mass of the sample by its volume. For example, a titanium sample that weighs 9.014 grams and occupies two cubic centimeters will have a density 4,507 kilograms per meter cubed: 9.014/1000/(2/1 x 10^6) = 4507.

Determine the ultimate strength of the material from the turning point of the material's stress-strain curve by tracing the stress-strain curve of the material until the curve reaches its highest point. The value read from the stress-axis, or y-axis, is the ultimate strength of the material.

Divide the density by the ultimate strength of the sample to obtain the weight-to-strength ratio of the material. For example, titanium has an ultimate strength of 434 x 10^6 N/m^2, and a density of 4507 kg/m^3. The weight-to-strength ratio for titanium is 1.04 x 10^-5 kg/Nm: 4507/434 x 10^6= 1.04 x 10^-5.

#### Things You'll Need

• Scale
• Measuring cylinder
• Water
• Ruler
• Calculator
• Stress-strain curve

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