Calculate specific weight and density for engineering and physics
kg (Mass)
lb (Mass)
Newtons (Force)
kN (Force)
lbf (Force)
Enter the mass or weight of the substance.
m³
cm³
ft³
in³
Liters
Gallons (US)
Enter the volume occupied by the substance.
Weight Density (Specific Weight)
1000.00 N/m³
Formula: Weight (Force) / Volume
Imperial Unit6.36 lbf/ft³
Kilo-Newtons1.00 kN/m³
Mass Density Equivalent101.97 kg/m³
Unit System
Value
Unit
SI (Standard)
1000.00
N/m³
SI (Heavy)
1.00
kN/m³
Imperial
6.36
lbf/ft³
CGS (Dyne)
10.00
dyne/cm³
*Chart compares your calculated weight density against standard specific weights of water and air.
What is a Weight Density Calculator?
A weight density calculator is a specialized engineering tool designed to compute the "specific weight" of a material. Unlike standard density, which measures mass per unit volume ($kg/m^3$), weight density measures the gravitational force exerted by a substance per unit volume ($N/m^3$ or $lbf/ft^3$).
This metric is crucial in fields like fluid mechanics, civil engineering, and structural analysis. Engineers use a weight density calculator to determine loads on structures, hydrostatic pressure in tanks, and buoyancy forces in fluids. While mass density remains constant regardless of location, weight density depends on the local acceleration of gravity.
Common misconceptions often arise between mass density and weight density. Mass density ($\rho$) quantifies how much matter is in an object, whereas weight density ($\gamma$) quantifies how heavy that matter is within a specific gravitational field.
Weight Density Formula and Mathematical Explanation
The core formula used in this weight density calculator is derived from the relationship between weight, mass, and volume. The symbol typically used for specific weight is the Greek letter Gamma ($\gamma$).
Primary Formula:
$\gamma = \frac{W}{V}$
OR
$\gamma = \rho \times g$
Variables Table
Variable
Meaning
SI Unit
Imperial Unit
$\gamma$ (Gamma)
Weight Density (Specific Weight)
$N/m^3$
$lbf/ft^3$
W
Total Weight (Force)
Newton ($N$)
Pound-force ($lbf$)
V
Total Volume
$m^3$
$ft^3$
$\rho$ (Rho)
Mass Density
$kg/m^3$
$slugs/ft^3$
g
Acceleration due to Gravity
$9.81 m/s^2$
$32.2 ft/s^2$
Practical Examples
Example 1: Water in a Storage Tank
An engineer needs to calculate the load on the floor of a tank containing 5 cubic meters of water. The total weight of the water is determined to be 49,050 Newtons.
Input Weight: 49,050 N
Input Volume: 5 $m^3$
Calculation: $49,050 / 5 = 9,810 N/m^3$
The weight density calculator confirms the specific weight is 9.81 $kN/m^3$, which is the standard value for water at 4°C.
Example 2: Civil Engineering Soil Sample
A soil sample has a volume of 2 cubic feet and weighs 220 pounds (force). The engineer wants to know the specific weight to check for compaction requirements.
Input Weight: 220 lbf
Input Volume: 2 $ft^3$
Calculation: $220 / 2 = 110 lbf/ft^3$
This result helps determining if the soil meets the density requirements for a road foundation.
How to Use This Weight Density Calculator
Select Input Type: Choose whether you are entering Mass (kg, lbs) or Force/Weight (Newtons, lbf). The calculator automatically handles the gravity conversion ($g = 9.81 m/s^2$) if you enter mass.
Enter Value: Input the numerical value for the mass or weight.
Enter Volume: Input the volume value and select the appropriate unit (cubic meters, liters, cubic feet, etc.).
Review Results: The primary result shows the Specific Weight in $N/m^3$.
Analyze Data: Check the "Mass Density Equivalent" if you need to convert back to $\rho$, or use the "Unit Conversions Table" for reporting in different standards.
Key Factors That Affect Weight Density Results
When using a weight density calculator, it is vital to understand that specific weight is not an intrinsic constant property like mass density. Several factors influence the final value:
Gravity ($g$): Since $\gamma = \rho \times g$, any change in gravitational acceleration changes the weight density. An object weighs less on the moon, so its weight density is lower there, even if its volume and mass remain the same.
Temperature: As temperature increases, substances (especially fluids) tend to expand, increasing their volume. Since volume is in the denominator ($\gamma = W/V$), an increase in volume leads to a decrease in weight density.
Pressure: For gases, pressure significantly increases density. Compressing a gas reduces its volume, thereby increasing its weight density. Liquids are generally considered incompressible, but at extreme depths, pressure can have a minor effect.
Material Composition: Impurities significantly alter density. Saltwater has a higher specific weight ($~10.1 kN/m^3$) than freshwater ($~9.81 kN/m^3$) due to the dissolved salt mass.
Humidity: Surprisingly, humid air is lighter (less dense) than dry air. Water vapor molecules are lighter than Nitrogen and Oxygen molecules, lowering the overall weight density of the air mixture.
Geographic Location: Gravity varies slightly across Earth's surface (stronger at poles, weaker at the equator). Precision engineering projects may require correcting standard gravity ($9.80665 m/s^2$) to local gravity.
Frequently Asked Questions (FAQ)
1. What is the difference between density and weight density?
Density (mass density) is mass per volume ($kg/m^3$), while weight density (specific weight) is weight per volume ($N/m^3$). They are related by gravity.
2. Why does the calculator ask for Mass vs Weight?
Physics distinguishes between Mass (amount of matter) and Weight (force of gravity). If you enter Mass, we multiply by gravity ($9.81 m/s^2$) to find the Weight Density.
3. What is the specific weight of water?
Standard specific weight of water is approximately $9,810 N/m^3$ or $62.4 lbf/ft^3$ at 4°C.
4. Can I calculate the weight of an object if I know its density?
Yes. If you know the weight density and the volume, multiply them ($\gamma \times V$) to get the total weight.
5. Does specific weight change in space?
Yes. In zero gravity, weight becomes zero, so specific weight (weight density) becomes zero, even though the object still has mass and mass density.
6. How do I convert $kg/m^3$ to $N/m^3$?
Multiply the mass density ($kg/m^3$) by gravitational acceleration ($9.81 m/s^2$) to get specific weight in $N/m^3$.
7. Which units does this weight density calculator support?
It supports SI units ($kg, N, m^3, L$) and Imperial units ($lbs, lbf, ft^3, in^3, gal$).
8. Is specific gravity the same as specific weight?
No. Specific Gravity is a unitless ratio comparing a substance's density to water's density. Specific Weight has units ($N/m^3$).