Fahrenheit to Celsius
- What is Fahrenheit?
- What is Celsius?
- What is Fahrenheit to Celsius Conversion?
- Formula to Convert Fahrenheit to Celsius
- Formula to Convert Celsius to Fahrenheit
- Derivation of Fahrenheit to Celsius Formula
- Fahrenheit to Celsius Chart
- Difference Between Fahrenheit and Celsius
- Summary
- Solved Example
- Practice Problem
- Frequently Asked Question
What is Fahrenheit?
Fahrenheit is a temperature scale used to measure how hot or cold something is. It's named after the German physicist Daniel Gabriel Fahrenheit, who invented it. On the Fahrenheit scale, water freezes at `32°` and boils at `212°` under standard atmospheric pressure. It's commonly used in the United States for everyday temperature measurements, like weather forecasts or cooking recipes.
What is Celsius?
Celsius is another temperature scale that measures how hot or cold something is. It's named after the Swedish astronomer Anders Celsius, who developed it. On the Celsius scale, water freezes at `0°` and boils at `100°` under standard atmospheric pressure. Celsius is widely used worldwide, especially in scientific contexts and everyday life outside of the United States.
What is Fahrenheit to Celsius Conversion?
Fahrenheit to Celsius refers to the process of converting a temperature given in the Fahrenheit scale to the Celsius scale. These two scales are widely used for measuring temperature and provide a standard way of measuring how hot or cold something is.
Learning how to switch between Fahrenheit and Celsius is important for many things. A few of them are listed below.
- When people talk about the weather, temperatures might be given in Fahrenheit or Celsius. Being able to convert between them helps us understand weather reports no matter which units they use.
- Additionally, in jobs like manufacturing or construction, temperature matters. Knowing how to convert between Fahrenheit and Celsius helps workers make sure machines are running safely and understand how materials expand or shrink with temperature changes.
- Even in school, students learn about converting temperatures. Being good at converting between Fahrenheit and Celsius helps them understand measurements better and solve problems in real life that involve temperature.
Formula to Convert Fahrenheit to Celsius
The formula to convert a temperature from Fahrenheit to Celsius is:
\(C = \frac{5}{9} \times (F - 32)\)
where
\(C\) is the temperature in Celsius,
\(F\) is the temperature in Fahrenheit.
Example: If the temperature outside is `77` degrees Fahrenheit, what is it in Celsius?
Solution:
Using the formula \(C = \frac{5}{9} \times (F - 32)\), we can plug in the Fahrenheit temperature given:
\(C = \left( 77 - 32 \right) \times \frac{5}{9}\)
\(C = 45 \times \frac{5}{9}\)
\(C ≈ 25\)
So, `77` degrees Fahrenheit is approximately `25` degrees Celsius.
Formula to Convert Celsius to Fahrenheit
The Celsius to Fahrenheit formula is \(F = (C \times \frac{9}{5}) + 32\), where \(C\) represents the temperature in Celsius and \(F\) represents the temperature in Fahrenheit. This formula allows you to convert temperatures from the Celsius scale to the Fahrenheit scale.
Example: Suppose you're traveling to a country where temperatures are usually given in Celsius, and you see a forecast of `25` degrees Celsius. You want to know what that temperature is in Fahrenheit. Use the Celsius to Fahrenheit conversion formula to tell the temperature in Fahrenheit.
Solution:
To convert Celsius to Fahrenheit formula, you can use the formula \(F = (C \times \frac{9}{5}) + 32\), where \(C\) is the temperature in Celsius and \(F\) is the temperature in Fahrenheit.
So, plugging in the value of `25` degrees Celsius into the formula:
\(F = (25 \times \frac{9}{5}) + 32\)
First, multiply `25` by \(\frac{9}{5}\):
\(F = (45) + 32\)
Now, add `32` to `45`:
\(F = 77\)
So, `25` degrees Celsius is equal to `77` degrees Fahrenheit.
Derivation of Fahrenheit to Celsius Formula
To derive the formula for converting Fahrenheit to Celsius, let's start with the two defining points on each scale:
`1`. Freezing point of water:
- Fahrenheit: `32°F`
- Celsius: `0°C`
`2`. The boiling point of water:
- Fahrenheit: `212°F`
- Celsius: `100°C`
Now, let's find the relationship between these two scales. Note that:
`1`. The difference between the freezing and boiling points of water in Fahrenheit is \(212°F - 32°F = 180°F\).
`2`. The difference between the freezing and boiling points in Celsius is \(100°C - 0°C = 100°C\).
Derivation of the Fahrenheit to Celsius formula takes into account the difference in freezing and boiling point of water in both the scales and the ratio between the scales. In order to derive the Fahrenheit to Celsius formula we can use the proportional relationship:
\( \frac{C - \text{Freezing Point in Celsius Scale}}{\text{Boiling Point in Celsius Scale}- \text{Freezing Point in Celsius Scale}} = \frac{F - \text{Freezing Point in Fahrenheit Scale}}{\text{Boiling Point in Fahrenheit Scale}- \text{Freezing Point in Fahrenheit Scale}} \)
Substituting the values, we get:
\( \frac{C - 0}{100- 0} = \frac{F - 32}{212- 32} \)
Simplifying the fractions, we get:
\( \frac{C}{100} = \frac{F - 32}{180} \)
Isolating the `C`, we get:
\( C = \frac{100}{180} (F - 32) \)
We can simplify this to:
\( C = \frac{5}{9} (F - 32) \)
Fahrenheit to Celsius Chart
Here's a chart showing the equivalent temperatures in Fahrenheit and Celsius:
Difference Between Fahrenheit and Celsius
Summary
`1`. Different Reference Points: Fahrenheit scale sets the freezing point of water at `32°F` and boiling point at `212°F`, while Celsius uses `0°C` for freezing point and `100°C` for boiling point.
`2`. Geographical Usage: Fahrenheit is predominantly used in the United States, while Celsius is the standard in most countries worldwide.
`3`. Conversion Formula: To convert Fahrenheit to Celsius, subtract `32` from the Fahrenheit temperature and then multiply by `5/9`.
`4`. Temperature Increments: Each degree Fahrenheit is equivalent to `5/9` of a degree Celsius, meaning Fahrenheit temperatures increase or decrease more rapidly.
`5`. Universal Understanding: Familiarity with Fahrenheit to Celsius conversion is essential for global communication, particularly in fields like meteorology, science, and international trade.
Solved Examples
Example `1`. Convert `77°F` to Celsius.
Solution:
`°C = 5/9 × (°F - 32)`
`°C = 5/9 × (77 - 32)`
`°C = 5/9 × 45`
`°C = 25`
Hence, `77°F = 25°C`.
Example `2`. What is the Celsius equivalent of `32°F` (freezing point of water)?
Solution:
`°C = (32 - 32) × 5/9`
`°C = 0 × 5/9`
`°C = 0`
Hence, the freezing point of water in Celsius is `0°C`.
Example `3`. A summer day in Phoenix, Arizona reaches `104°F`. What is the temperature in Celsius?
Solution:
`°C = (104 - 32) × 5/9`
`°C = 72 × 5/9`
`°C = 40`
So, the temperature in Arizona reaches `40°C` during the summer day.
Example `4`. You set your oven to `400°F` to bake cookies. What is the equivalent temperature in Celsius?
Solution:
`°C = (400 - 32) × 5/9`
`°C = 368 × 5/9`
`°C = 204.4`
The equivalent temperature in Celsius is `204.4 °C`.
Example `5`. Body temperature is typically around `98.6°F` Convert this to Celsius to understand the human body temperature in Celsius.
Solution:
`°C = (98.6 - 32) × 5/9`
`°C = 66.6 × 5/9`
`°C = 37.2`
Therefore, the normal human body temperature is around `37.2°C`.
Practice Problems
Q`1`. Which temperature is closest to `20°C`?
- `32°F`
- `68°F`
- `86°F`
- `104°F`
Answer: b
Q`2`. A recipe calls for baking a cake at `175°C`. What is the closest equivalent temperature in Fahrenheit?
- `250°F`
- `300°F`
- `350°F`
- `400°F`
Answer: c
Q`3`. Water boils at `100°C`. What is the boiling point of water in Fahrenheit?
- `180°F`
- `212°F`
- `248°F`
- `284°F`
Answer: b
Q`4`. Today's temperature in London is a chilly `5°C`. What is the closest temperature in Fahrenheit?
- `32°F`
- `41°F`
- `50°F`
- `59°F`
Answer: b
Q`5`. You want to set your thermostat to `70°F`. What is the closest temperature in Celsius?
- `15°C`
- `20°C`
- `25°C`
- `30°C`
Answer: b
Frequently Asked Questions
Q`1`. Why do we need to convert Fahrenheit to Celsius?
Answer: Fahrenheit and Celsius are two common temperature scales used worldwide. Converting between them allows for universal understanding and communication, especially in global contexts like international trade, travel, scientific research, weather changes, etc.
Q`2`. How do I convert Fahrenheit to Celsius?
Answer: To convert Fahrenheit to Celsius, subtract `32` from the Fahrenheit temperature and then multiply by `5/9`. The formula is: \(C = (F - 32) \times \frac{5}{9}\), where \(C\) is the temperature in Celsius and \(F\) is the temperature in Fahrenheit.
Q`3`. What is the freezing and boiling point of water in Fahrenheit and Celsius?
Answer: In Fahrenheit, water freezes at `32°F` and boils at `212°F`. In Celsius, water freezes at `0°C` and boils at `100°C`. These reference points are crucial for understanding the scales and converting temperatures between them.
Q`4`. Which countries use Fahrenheit and which use Celsius?
Answer: Fahrenheit is primarily used in the United States, while Celsius is more commonly used in most other countries worldwide. However, Celsius is also officially adopted by scientific communities in the US and is often used in scientific research.
Q`5`. Why are there two different temperature scales?
Answer: Fahrenheit and Celsius were developed independently based on different reference points and historical contexts. Fahrenheit was developed by Daniel Gabriel Fahrenheit, whereas Celsius was developed by Anders Celsius. The adoption of different scales reflects historical, cultural, and scientific differences among regions.