How to Convert Fahrenheit to Celsius: Step-by-Step Formula and Examples
Temperature is an essential physical quantity used to measure how hot or cold an object or environment is. Two of the most popular temperature scales are Celsius (°C) and Fahrenheit (°F). These scales are widely used for weather reporting, science experiments, and daily life measurements. Understanding their relationship is crucial for students, especially when converting temperatures in Physics problems and practical situations.
What Are Celsius and Fahrenheit Scales?
The Celsius scale was introduced by Anders Celsius. It is based on the freezing point of water at 0°C and the boiling point at 100°C under standard atmospheric pressure. The Fahrenheit scale, developed by Daniel Gabriel Fahrenheit, sets water’s freezing point at 32°F and boiling point at 212°F. Both scales are linear but use different zero points and scale divisions.
How to Convert Between Celsius and Fahrenheit
To accurately convert a temperature from one scale to another, it is important to use the correct formulas. The conversion is not simply proportional because the zero points and increments are different for each scale.
| Conversion | Formula | Description |
|---|---|---|
| Celsius to Fahrenheit | F = (9/5 × C) + 32 | Multiply Celsius by 9/5, then add 32 |
| Fahrenheit to Celsius | C = 5/9 × (F − 32) | Subtract 32 from Fahrenheit, then multiply by 5/9 |
Solved Examples
Let us understand the conversion process with step-by-step examples:
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Example 1: Convert 12°F to Celsius
C = 5/9 × (F – 32)
C = 5/9 × (12 – 32)
C = 5/9 × (–20)
C = –100/9
C ≈ –11.11°C
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Example 2: Convert 30°C to Fahrenheit
F = (9/5 × C) + 32
F = (9/5 × 30) + 32
F = (54) + 32
F = 86°F
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Example 3: What is 1°F in Celsius?
C = 5/9 × (1 – 32)
C = 5/9 × (–31)
C = –17.22°C
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Example 4: What is 1°C in Fahrenheit?
F = (9/5 × 1) + 32
F = 1.8 + 32
F = 33.8°F
Historical Background
The Fahrenheit scale was invented first by Daniel Gabriel Fahrenheit in 1724. He used the freezing point of a saltwater solution (brine) as 0°F and estimated body temperature close to 96°F. The Celsius scale was developed later in 1742 by Anders Celsius as a centigrade scale, with 0°C as the melting point of snow and 100°C as the boiling point of water.
| Scale | Freezing Point of Water | Boiling Point of Water | Common Symbol |
|---|---|---|---|
| Celsius | 0°C | 100°C | °C |
| Fahrenheit | 32°F | 212°F | °F |
Key Concept: When Are Celsius and Fahrenheit Equal?
There is a point where both Celsius and Fahrenheit values are numerically the same. To find this, set C = F in the formula:
C – (9/5 × C) = 32
(–4/5)C = 32
C = –40
Thus, –40°C is equal to –40°F.
Quick Celsius to Fahrenheit Conversion Chart
| Celsius (°C) | Fahrenheit (°F) |
|---|---|
| –40 | –40 |
| 0 | 32 |
| 10 | 50 |
| 20 | 68 |
| 25 | 77 |
| 30 | 86 |
| 100 | 212 |
Step-by-Step Approach for Solving Temperature Conversion Problems
- Identify which scale you need to convert from and to.
- Use the correct formula:
For Celsius to Fahrenheit: F = (9/5 × C) + 32
For Fahrenheit to Celsius: C = 5/9 × (F − 32) - Substitute the given temperature value.
- Solve the equation step by step.
- Write the final answer with correct units.
Applications of Fahrenheit and Celsius Scales
- Weather reporting and forecasting.
- Temperature control in home appliances and ovens.
- Measuring body temperature in clinical settings.
- Science laboratory experiments and Physics calculations.
Practice Questions
- Convert 50°C to Fahrenheit.
- A liquid is at 68°F. What is this temperature in Celsius?
- Find the Fahrenheit value when the Celsius temperature is 100°C.
Explore More Physics Topics
Mastering temperature scale conversions is a fundamental skill in Physics. Remember to use the formulas carefully and always write your final answers with the correct units for each scale. For more practice, study similar Physics concepts on Vedantu and apply these methods to solve different thermodynamics problems efficiently.
FAQs on Relation Between Fahrenheit and Celsius: Key Formulas & Conversion
1. What is the fundamental relationship between the Fahrenheit and Celsius scales?
The fundamental relationship is based on different reference points and degree sizes for each scale:
• Celsius scale: Freezing point of water is 0°C; boiling point is 100°C.
• Fahrenheit scale: Freezing point is 32°F; boiling point is 212°F.
• The mathematical relationship is:
F = (9/5) × C + 32
C = (5/9) × (F - 32)
2. What is the formula to convert a temperature from Celsius to Fahrenheit?
To convert Celsius (°C) to Fahrenheit (°F), use:
• °F = (°C × 9/5) + 32
First multiply the Celsius value by 9/5 (or 1.8), then add 32 to get Fahrenheit.
3. How do you convert a temperature from Fahrenheit back to Celsius?
To convert Fahrenheit (°F) to Celsius (°C):
• °C = (°F − 32) × 5/9
Subtract 32 from the Fahrenheit temperature, then multiply by 5/9 for the Celsius value.
4. Why is 32 subtracted in the Fahrenheit to Celsius conversion formula?
32 is subtracted because it aligns the freezing point of water for both scales:
• 0°C equals 32°F (freezing point of water)
• Subtracting 32 ensures the correct offset between the two scales before applying the ratio.
5. What does the 9/5 ratio in the temperature conversion formula represent?
The 9/5 ratio matches the size of degrees between scales:
• Water boils at 100°C and 212°F (a 100°C range vs. 180°F)
• 180/100 = 9/5, showing one Celsius degree is equal to 1.8 Fahrenheit degrees.
6. How does the Kelvin scale relate to Celsius and Fahrenheit?
The Kelvin (K) scale is the absolute temperature scale, directly related to Celsius:
• K = °C + 273.15
• To convert Fahrenheit to Kelvin, first use the F to C formula, then C to K.
• Kelvin does not use the degree prefix and starts at absolute zero.
7. At what temperature do the Celsius and Fahrenheit scales show the same numerical reading?
The Celsius and Fahrenheit readings are equal at -40 degrees:
• -40°C = -40°F
This is the only point where the numbers coincide on both scales.
8. Is the relation between Celsius and Fahrenheit direct or proportional?
The relation is linear but not directly proportional:
• There is a fixed offset of 32° between the scales.
• Increases or decreases are proportional after accounting for the offset (i.e., after aligning zero points).
9. How do you quickly estimate temperature conversion between Celsius and Fahrenheit?
For a quick estimate:
• Double the Celsius temperature and add 30 to approximate Fahrenheit: F ≈ 2C + 30
• For exact conversion, always use the official formula.
10. What are the main differences between Celsius, Fahrenheit, and Kelvin temperature scales?
Main differences include their zero points and degree intervals:
• Celsius: 0°C = water freezes, 100°C = boils
• Fahrenheit: 32°F = water freezes, 212°F = boils
• Kelvin: 0 K = absolute zero, 273.15 K = water freezes, 373.15 K = boils
• Kelvin uses no degree symbol and is used in scientific contexts.
11. In which real-world applications is the Fahrenheit scale still primarily used?
Fahrenheit is mainly used in the United States and related territories for:
• Weather forecasts
• Household temperature measurements (cooking, ovens)
• Body temperature readings
Most countries and scientific fields use Celsius or Kelvin.
12. Why is accurate temperature conversion important in Physics and exams?
Accurate conversion is essential for:
• Solving thermodynamics questions and equations
• Ensuring correct laboratory results and scientific communication
• Avoiding calculation errors and penalties in exams like JEE, NEET, and board assessments
Using the correct formula ensures reliable and consistent answers.
