Volumenrechner
Berechne das Volumen jeder 3D-Form sofort
Volume Calculator
Calculate the volume of common 3D shapes
Enter the radius to calculate volume
V = (4/3) x pi x r^3What is a Volume Calculator?
A Volume Calculator is a geometry tool that measures the volume of a 3D object. Volume is the amount of space an object occupies or the amount of material it can hold (like water in a tank). It's used in everyday tasks like estimating how much concrete you need for a slab, how much soil fills a planter, how much water fits in a pool, or how much storage space is inside a container.
Unlike area (which measures flat surfaces), volume applies to three-dimensional shapes and is always expressed in cubic units, such as cubic inches (in³), cubic feet (ft³), cubic centimeters (cm³), or cubic meters (m³). If you enter measurements in feet, the output will be in cubic feet; if you enter measurements in meters, the output will be in cubic meters.
A volume calculator helps you avoid common mistakes such as using the wrong formula for a shape, mixing units, or confusing radius with diameter. It's useful for students learning geometry and for real-world planning, construction, and engineering.
Common 3D Shapes for Volume Calculations:
- Sphere -- radius
- Cube -- side length
- Rectangular Prism (Box) -- length, width, height
- Cylinder -- radius and height
- Cone -- radius and height
- Pyramid -- base area and height
How to Use This Volume Calculator
- Select the 3D shape -- choose the shape you want to calculate (e.g., sphere, cube, cylinder)
- Enter the required dimensions -- such as radius, length, width, height, or diameter
- Choose units if supported -- in, ft, cm, m, etc.
- Click 'Calculate' -- to compute the volume
- Review the result -- confirm it is shown in cubic units
Tips:
- Use consistent units across all inputs (don't mix inches and feet unless you convert)
- If a formula uses radius, make sure you are not entering diameter by mistake (diameter = 2 × radius)
- For liquid capacity, you may want to convert cubic units into liters or gallons after calculating
Volume Formulas
Below are common volume formulas for popular 3D shapes.
Cube
V = s³
Where s = side length
Rectangular Prism (Box)
V = l × w × h
Where l = length, w = width, h = height
Cylinder
V = πr²h
Where r = radius, h = height, π ≈ 3.14159
Sphere
V = (4/3)πr³
Where r = radius
Cone
V = (1/3)πr²h
Where r = radius, h = height
Pyramid (General)
V = (1/3)Bh
Where B = base area, h = vertical height
Example Calculations
Example 1: Rectangular Prism Volume
Length: 10 ft, Width: 4 ft, Height: 3 ft
Calculation: V = 10 × 4 × 3 = 120
Result: 120 ft³
Example 2: Cube Volume
Side length: 5 cm
Calculation: V = 5³ = 125
Result: 125 cm³
Example 3: Cylinder Volume
Radius: 3 m, Height: 10 m
Calculation: V = π × 3² × 10 = π × 9 × 10 = 90π ≈ 282.74
Result: Volume ≈ 282.74 m³
Example 4: Sphere Volume
Radius: 6 in
Calculation: V = (4/3)π × 6³ = (4/3)π × 216 = 288π ≈ 904.78
Result: Volume ≈ 904.78 in³
Frequently Asked Questions
What's the difference between volume and capacity?
Volume is the amount of 3D space an object occupies. Capacity usually refers to how much a container can hold (liquid or material). In many cases they're closely related, but 'capacity' is often used for containers.
What units is volume measured in?
Volume is measured in cubic units such as in³, ft³, cm³, and m³. For liquids, volume is often converted to liters (L) or gallons (gal).
Why do I get a huge number compared to my inputs?
Volume grows with three dimensions, so values can increase quickly. Also check that you didn't accidentally enter units incorrectly (inches vs feet) or use diameter instead of radius.
How do I convert cubic units to liters or gallons?
After finding volume in a cubic unit, you can convert using standard conversion factors. For example, 1,000 cm³ = 1 liter. If you need this often, a unit converter tool can help.
What if I don't know the exact shape?
Many real-world objects can be approximated by common shapes. For example, a tank might be approximated as a cylinder, and a box-shaped container as a rectangular prism. Use the closest shape and measurements you can for a practical estimate.
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Was ist Volumen?
Volumen ist die Menge des dreidimensionalen Raums, den ein fester Koerper einnimmt. Es gibt an, wie viel ein Behaelter fassen kann oder wie viel Material eine Form ausmacht. Volumen wird immer in Kubikeinheiten gemessen - Kubikzentimeter (cm3), Kubikmeter (m3), Kubikfuss (ft3) usw. Es ist eine grundlegende Messung, die taeglich in Verpackung, Transport, Kochen, Bauwesen und Wissenschaft verwendet wird.
Dieser Rechner unterstuetzt sechs der gaengigsten 3D-Formen: Kugel, Zylinder, Kegel, Wuerfel, Quader (Box) und Pyramide. Waehle einfach deine Form, gib die erforderlichen Abmessungen ein, und das Ergebnis erscheint sofort zusammen mit der verwendeten Formel. Egal ob du Student, Ingenieur oder einfach neugierig bist, wie viel Erde in einen Blumentopf passt - dieses Tool hilft dir weiter.
So verwendest du den Volumenrechner
- Waehle die 3D-Form, die du berechnen moechtest: Kugel, Zylinder, Kegel, Wuerfel, Box oder Pyramide.
- Gib die erforderlichen Abmessungen fuer diese Form ein (Radius, Hoehe, Seitenlaenge, Grundflaeche usw.).
- Klicke auf Berechnen, um das Volumen zu ermitteln.
- Lies das Ergebnis in Kubikeinheiten ab (cm3, m3, ft3 oder welche Einheit du eingegeben hast).
Volumenformeln
Kugel: V = (4/3)*pi*r3
Zylinder: V = pi*r2*h
Kegel: V = (1/3)*pi*r2*h
Wuerfel: V = s3
Quader: V = l x w x h
Pyramide: V = (1/3) x Grundflaeche x hAlle Abmessungen muessen vor der Berechnung in derselben Einheit angegeben werden. Das Ergebnis erscheint in der entsprechenden Kubikeinheit - wenn du zum Beispiel Zentimeter eingibst, wird das Volumen in cm3 ausgegeben.
Geloeste Beispiele
Kugel mit Radius 3 cm
Mit V = (4/3)*pi*r3: V = (4/3) * pi * 27 ca. 113,10 cm3. Eine Kugel mit einem Radius von 3 cm nimmt etwa 113 Kubikzentimeter Raum ein.
Zylinder mit Radius 5 cm und Hoehe 10 cm
Mit V = pi*r2*h: V = pi * 25 * 10 ca. 785,40 cm3. Eine zylindrische Dose mit diesen Abmessungen fasst etwa 785 cm3 - knapp unter einem Liter.
Quader 4 m x 3 m x 2 m
Mit V = l x w x h: V = 4 * 3 * 2 = 24 m3. Ein Lagerraum oder Container mit diesen Abmessungen hat ein Gesamtvolumen von 24 Kubikmetern.