Specific Weight Calculator

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Density ρ (kg/m³)

Gravity g (m/s²)

Results

Specific Weight (γ)

9,806.65

N/m³

Specific weight (kN/m³)	9.8066 kN/m³
Formula	γ = ρ × g

What Is Specific Weight?

Specific weight (also called unit weight), symbol \(\gamma\), is the weight of a substance per unit volume. It is closely related to density but accounts for gravity: while density \(\rho\) measures mass per unit volume, specific weight measures force (weight) per unit volume. The SI unit is the newton per cubic metre (N/m³). This calculator works for any fluid or solid material — water, oil, mercury, soil, concrete — and on any planet, since you can change the gravitational acceleration.

Specific weight is the weight of fluid per unit volume, combining density and gravity.

How to Use the Calculator

Enter the density \(\rho\) of the material in kilograms per cubic metre (kg/m³) and the local gravitational acceleration \(g\) in metres per second squared (m/s²). On Earth, \(g\) is approximately 9.80665 m/s² (the standard value, pre-filled). Press calculate to get the specific weight in both N/m³ and kN/m³.

The Formula Explained

The governing equation is:

$$\gamma = \rho \cdot g$$

Here \(\rho\) is density in kg/m³ and \(g\) is acceleration due to gravity in m/s². Multiplying a mass-per-volume by an acceleration gives a force-per-volume, which is exactly what specific weight represents. Because \(1\ \text{kg}\cdot\text{m/s}^2 = 1\ \text{N}\), the result naturally comes out in N/m³.

The formula \(\gamma = \rho \cdot g\) multiplies density by gravitational acceleration.

Worked Example

Fresh water has a density of about 1000 kg/m³. Using standard Earth gravity \(g = 9.80665\ \text{m/s}^2\):

$$\gamma = 1000 \times 9.80665 = 9806.65\ \text{N/m}^3 \approx 9.81\ \text{kN/m}^3.$$

This matches the well-known specific weight of water of roughly 9.81 kN/m³ at standard conditions.

FAQ

Is specific weight the same as density? No. Density is mass per volume (kg/m³); specific weight is weight (force) per volume (N/m³). They are linked by gravity: \(\gamma = \rho g\).

Does specific weight change on the Moon? Yes. Density stays the same, but because lunar gravity is about 1.62 m/s², the specific weight is about one sixth of its Earth value.

What value of g should I use? For most engineering on Earth, 9.81 m/s² (or the standard 9.80665 m/s²) is appropriate. Use the local value for high-precision work.