Skip to content
Calcapedia
Menu
Science

Density Calculator

Solve for density, mass or volume from the other two, in kg/m³, g/cm³ or lb/ft³.

Level: Grades 8–9

  • Common Core standard HSG.MG.A.2Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).
Printable worksheet

Density Calculator

Know the answer you need? Pick an input to work backward.

Inputs
Solve for

Result

Density

2,700 kg/m³

Density is 2,700 kg/m³.

Density in g/cm³
2.7 g/cm³
Density in lb/ft³
168.5555 lb/ft³

See the step-by-step solution ↓

Step-by-step solution

  1. Change the volume to m³ so all the units match before using the formula (1 L = 0.001 m³)

    1 L×0.001=0.001 m³

  2. Divide the mass by the volume to get the density

    2.70.001=2,700 kg/m³

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Find the density, mass or volume of something when you know the other two. Density tells you how much mass (roughly, how heavy it is) is packed into a given space. It's written ρ (the Greek letter rho), and it's mass divided by volume. A liter of water has a mass of about one kilogram. A liter of aluminium is about 2.7 kilograms, so aluminium is roughly 2.7 times as dense.

Since the formula links three amounts, you can find any one from the other two. Choose what you want to solve for. Enter the two values you know, in whatever units you have, and pick the unit for the answer. The calculator changes everything to SI units (the metric units scientists use: kilograms and cubic meters). Then it applies the formula and changes the answer back, showing each step.

Where it's used

Why this math matters outside the classroom:

  • Identifying metals. A 270 g block that displaces 100 cm³ of water has a density of 2.7 g/cm³, the value for aluminum.
  • Shipping loads. Haulers estimate a load's weight from its volume, so 2 m³ of dry sand at about 1,600 kg/m³ weighs around 3,200 kg.
  • Float or sink. Students predict whether objects float by comparing their density with water's 1 g/cm³.
  • Checking gold. Jewelers test a gold piece by weighing it in air and in water, since pure gold's density is about 19.3 g/cm³.

Grade level and standards: Grades 8–9; Common Core State Standards for Mathematics HSG.MG.A.2. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Choose whether to solve for density, mass or volume.
  2. Enter the two values you know and choose a unit for each.
  3. Choose the unit you want the answer in. The result is also listed in the other units.

What the inputs mean

Density (ρ)
1 g/cm³ equals 1,000 kg/m³, and is the same as 1 kg per liter or 1 g per mL.
Mass (m)
1 lb is exactly 0.45359237 kg.
Volume (V)
1 liter is 1,000 cm³ (or mL), and 1 m³ is 1,000 liters. A cubic foot is about 28.32 liters.

Formula and method

ρ = m ÷ V
m = ρ × V
V = m ÷ ρ
1 g/cm³ = 1,000 kg/m³;  1 lb/ft³ ≈ 16.0185 kg/m³

In the formulas, ρ is the density, m is the mass and V is the volume. All three are the same rule, just rearranged. The calculator first changes your inputs to kilograms, cubic meters and kilograms per cubic meter, so the units always match.

The pound-per-cubic-foot factor comes from two exact definitions: 1 lb = 0.45359237 kg and 1 ft = 0.3048 m. Together they give 0.45359237 ÷ 0.028316846592 = 16.0184634 kg/m³.

Worked example

A solid block has a mass of 2.7 kg and a volume of 1 liter. What is its density?

  1. Change the volume to cubic meters: 1 L × 0.001 = 0.001 m³.
  2. Density = mass ÷ volume = 2.7 ÷ 0.001 = 2,700 kg/m³.
  3. In other units, that's 2.7 g/cm³ or about 168.56 lb/ft³.

Result: The block's density is 2,700 kg/m³, which matches aluminium.

Understanding the result

Compare a density with water's (about 1,000 kg/m³ or 1 g/cm³) to tell whether a solid object will sink or float in water. This works as long as the object has no hollow spaces.

Density belongs to the material, not the object. A small piece and a large piece of the same metal have the same density.

Assumptions and limitations

  • The material is the same all the way through, so one density describes all of it.
  • Mass and volume are measured at the same temperature and pressure.
  • Gases change density a lot with temperature and pressure. This calculator doesn't apply any gas law to account for that.
  • Objects with holes or hollow spaces give an average (bulk) density, not the density of the solid material.
  • Liquids and solids also expand slightly as they warm up. That's why reference densities are given at a stated temperature.

Frequently asked questions

How do I convert g/cm³ to kg/m³?

Multiply by 1,000. A cubic meter holds one million cubic centimeters, and a kilogram is 1,000 grams. Put together, those make a factor of 1,000. For example, 7.85 g/cm³ is 7,850 kg/m³.

What is the density of water?

Close to 1,000 kg/m³ (1 g/cm³ or about 62.4 lb/ft³). It changes slightly with temperature. It's highest near 4 °C and a little lower at room temperature.

How do I find the volume of an irregular object?

Put it all the way under water and measure how much the water level rises, or how much water spills out. Then divide its mass by that volume to get its density.

Is density the same as specific gravity?

Not quite. Specific gravity is density divided by the density of water, so it has no units. A density of 2.7 g/cm³ matches a specific gravity of about 2.7.

How this calculator is checked

Method: Definition of density, ρ = m/V, with exact SI and US customary conversion factors. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

Embed this calculator

Put this Density Calculator on your own website or blog for free. Paste this code where you want it to appear: