Verhältnisrechner
Verhältnisse kürzen, vergleichen und auf jeden Zielwert skalieren
Ratio Calculator
Simplify and solve ratios
Simplify a ratio A:B to its lowest terms
Divide both A and B by their GCDWhat is a Ratio Calculator?
A Ratio Calculator is a math tool that helps you compare two or more quantities and express their relationship in a simple form. A ratio shows how much of one thing there is compared to another. Ratios are commonly written using a colon, such as 3:2, or as a fraction, such as 3/2.
Ratios are used in everyday life and many fields: cooking recipes (2 cups flour to 1 cup sugar), mixing solutions (1 part concentrate to 4 parts water), map scales, financial comparisons, and geometry. They are especially useful when you need to scale something up or down while keeping the same relationship between values.
A ratio calculator can simplify ratios, create equivalent ratios, and help solve 'missing value' problems (often called proportion problems). It saves time and reduces mistakes when working with large numbers or decimals.
How to Use This Ratio Calculator
- Enter the ratio values -- Input the two (or more) numbers you want to compare (example: 24 and 36)
- Choose an option (if available) -- such as simplify ratio, find equivalent ratio, or solve for missing value
- Click 'Calculate' -- the calculator processes the ratio
- Review the simplified ratio -- example: 24:36 becomes 2:3
- Use the result -- apply the ratio for scaling recipes, mixing, comparing quantities, or solving proportions
Tips:
- Ratios work best when the values represent the same type of measurement (e.g., both in grams, both in dollars)
- If you use decimals, the calculator may convert them to a simplified whole-number ratio
- If a ratio is used to scale something (like a recipe), make sure you multiply or divide both parts by the same factor
Ratio Formulas
Ratio Simplification
To simplify a ratio a:b, divide both numbers by their greatest common divisor (GCD):
Simplified = (a / gcd(a,b)) : (b / gcd(a,b))
Example: a = 24, b = 36
gcd(24, 36) = 12
24:36 → (24/12):(36/12) = 2:3
Equivalent Ratios
Multiply or divide both parts by the same number k:
(a:b) → (a × k : b × k)
2:3 × 5 → 10:15
Proportions (Missing Value)
A proportion compares two equal ratios: a/b = c/d
Solve using cross-multiplication:
a × d = b × c
If d is unknown: d = (b × c) / a
Example Calculations
Example 1: Simplify a Ratio
Input: 24:36
GCD: gcd(24, 36) = 12
Calculation: 24 ÷ 12 = 2, 36 ÷ 12 = 3
Result: 2:3
Example 2: Create an Equivalent Ratio
Input: 3:8, scaled by 4
Calculation: 3 × 4 = 12, 8 × 4 = 32
Result: 12:32 (simplifies back to 3:8)
Example 3: Recipe Scaling (Real-World Use)
Setup: A drink mix uses a ratio of 1:5 (concentrate : water)
Problem: If you have 3 cups of concentrate, how much water?
Calculation: 1 part → 5 parts, so 3 parts → 3 × 5 = 15 parts
Result: 15 cups of water
Example 4: Solve a Proportion (Missing Value)
Problem: Solve for x in 2/3 = 10/x
Cross-multiply: 2x = 3 × 10 = 30
Solve: x = 30 ÷ 2 = 15
Result: x = 15
Frequently Asked Questions
What's the difference between a ratio and a fraction?
A fraction represents a part of a whole (3/4). A ratio compares two quantities (3:4). Ratios can be written as fractions, but they often represent comparisons rather than parts.
How do I simplify a ratio?
Divide both parts by their greatest common divisor (GCD). For example, 18:24 simplifies to 3:4 because gcd(18,24) = 6, and 18/6 = 3, 24/6 = 4.
Can ratios include more than two numbers?
Yes. You can have ratios like 2:3:5, often used to compare three quantities (for example, ingredient proportions). Simplification usually divides all terms by their common factor.
What does a ratio like 1:5 mean?
It means for every 1 unit of the first quantity, there are 5 units of the second. For example, 1 cup of concentrate to 5 cups of water.
What is a proportion, and why is it useful?
A proportion states that two ratios are equal (a/b = c/d). It's useful for scaling, converting, and solving for unknown values in real-world situations like recipes, maps, and unit conversions.
Want to add this ratio calculator to your website? Get a custom embed code that matches your site's design and keeps visitors engaged.
Was ist ein Verhältnis?
Ein Verhältnis drückt die Beziehung zwischen zwei Größen aus. In der Form A:B (oder A/B) geschrieben, zeigt es, wie oft ein Wert den anderen enthält. Verhältnisse begegnen uns überall: Bildschirmformate (16:9), Rezeptmengen (1:2 Mehl zu Zucker), Finanzkennzahlen bei Investitionen und Kartenmaßstäbe (1:50.000), die es ermöglichen, reale Entfernungen auf Papier zu messen.
Dieser Rechner kürzt Verhältnisse auf ihre kleinste Form, indem beide Teile durch ihren größten gemeinsamen Teiler (ggT) dividiert werden. Er vergleicht außerdem zwei Verhältnisse darauf, ob sie gleichwertig sind, und skaliert ein Verhältnis auf eine beliebige Gesamtmenge — so siehst du sofort, wie viel du von jedem Teil brauchst, wenn sich die Zielmenge ändert.
So verwendest du den Verhältnisrechner
- Gib die beiden Werte des Verhältnisses ein — A und B.
- Wähle die Operation: kürzen, vergleichen oder skalieren.
- Zum Skalieren gibst du die Gesamtmenge ein, die du erreichen möchtest.
- Klicke auf Berechnen, um das gekürzte oder skalierte Ergebnis sofort zu sehen.
Formeln und Referenz
Kürzen von A:B — beide durch ggT(A, B) teilen
Beispiel: 12:8 → ggT = 4 → 3:2
Gleichwertige Verhältnisse — Kreuzprodukt prüfen
A:B = C:D wenn A × D = B × C
Skalieren auf Gesamtmenge T:
Teil A = (A / (A + B)) × T
Teil B = (B / (A + B)) × T
Teil zum Ganzen:
A / (A + B) = Anteil von A an der GesamtmengeEin Verhältnis A:B entspricht dem Bruch A/(A+B) als Anteil am Ganzen oder A/B als direktem Vergleich der beiden Teile.
Durchgerechnete Beispiele
15:10 kürzen
ggT(15, 10) = 5. Beide Seiten dividieren: 15 ÷ 5 = 3, 10 ÷ 5 = 2. Gekürztes Verhältnis: 3:2. Auf je 3 Einheiten von A kommen 2 Einheiten von B.
Zement und Sand im Verhältnis 3:5 für 40 kg gesamt mischen
Gesamtteile = 3 + 5 = 8. Zement = (3/8) × 40 = 15 kg. Sand = (5/8) × 40 = 25 kg. Probe: 15 + 25 = 40 kg. ✓
Bildschirmformat 1920:1080 gekürzt
ggT(1920, 1080) = 120. Beide dividieren: 1920 ÷ 120 = 16, 1080 ÷ 120 = 9. Ergebnis: 16:9 — das Standard-Breitbildformat, das auf fast allen modernen Bildschirmen verwendet wird.