Another Angle on How to Calculate and Measure Angles

Angles are all over our world.  Without the knowledge of how to measure and calculate between angles, we would have a difficult time engineering and using them in our everyday lives.  One of the most important shapes in the engineering world is the triangle.  Just the name itself is made up of tri (three) and angle.  It's fairly self-descriptive.  But, moving on, let's look at how angles are measured.

The first measurement of an angle is in regards to slope.  If you look at the roof on your house you'll notice that it probably has an angle to it.  This angle is called slope and is measured in the amount of rise for a given amount of run.  In other words, for every unit of lenght you have horizontally, how many units of height are there?  A slope can also be described as pitch or percentage of slope.  The percentage is the amount of rise

divided by the amount of run.  If your roof slope goes up 6 inches for every 12 inches of horizontal run, you have a 50% slope.

Another way of calculating an angle is with radians.  If you take the radius of a circle and apply that length distance around the circumference of the circle, it will make a pie shape.  The angle formed by that shape is one radian.  Because it is related to the circle, you can also look at it this way.  There are 2 x Pi radians in a full circle.  That's approximately 6.28 radians.  It's easiest to look at an illustration.


 The final, and most common way of measuring an angle is with degrees.  Again, we refer to a circle.  Every circle has 360 degrees.  An angle that is 90 degrees takes up on quarter of a circle and is also known as a right angle.

When you measure angles it is important to know what type of measurement is being used and how to decipher between them.  After all if someone gives you a slope of 45 degrees, what would that convert to in a percentage?  For more on how to convert between different angle measurements try the online conversion calculators below.

Degrees to Slope Percentage Calculator

Slope Percentage to Degrees Calculator

Degrees to Radians Calculator

Radians to Degrees Calculator

More Geometry Calculators

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

Your Carbon Footprint. Would You Describe It as Bigfoot?

Everyone has a Carbon Footprint.  If you are a consumer of energy that is created by fossil fuels, then there is an attributable amount of CO₂ emissions that you have some responsibility for.  Even if you used solar panels on your house, drive an electric car, and think that everything you use is "green", you are still benefiting from the use of fossil fuels.

If you were able to cut out all of the energy usage in your life that is generated by fossil fuels, you still are indirectly benefiting from them.  Do you use roads?  The more you use roads, the more they wear and need maintenance.  What kinds of fuel do the maintenance vehicles use to repair roads?  What about groceries?  Do you buy groceries at the store?  What kinds of fuels were used to deliver those goods?  What about the farm equipment that harvested the food?  Those machines burn fossil fuels.

Ignoring the indirect ways that you might utilize the usage of fossil fuels, we can fairly accurately determine the amount of emissions are directly related to your daily life based on your household usage of electricity and natural gas, and your monthly fuel consumption in your vehicle.  For your natural gas and electricity usage, you simply need your latest bills to see how much you use.  For your vehicle, try to keep track of the total amount of gallons of fuel you use in a month.  If that's too difficult, take your average MPG and multiply that by an estimate of the total amount of miles you drive.  There are fuel mileage calculators to help with this kind of mathematical problems.

Once you have tallied the total amount of energy usage that is directly related to your household needs and your vehicle usage, you can calculate your total Carbon Footprint.  A Carbon Footprint Calculator will help determine how many pounds of CO₂ emissions per month, or year, you will release into the environment.

There are ways that people are offsetting their Carbon Footprint.  One of the most popular ways utilizes trees in a process called Carbon Sequestration.  Trees naturally absorb CO₂ and release oxygen back into the environment.  You only need to know how many trees it takes to offset your Carbon Footprint.  Every tree is different and absorb these emissions at different rates depending on type and age.  To help estimate how many trees it would take to offset your Carbon Footprint try this Carbon Offset Calculator.  This should give you a better idea of what impact you have on the environment.

Of course, taking steps to reduce the amount of energy you consume is obviously going to have the most significant impact on the environment.  How does your Carbon Footprint compare with your friends?

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

Absolute Zero Sounds Pretty Cold....And It Is!

Absolute Zero is a term that is mostly used in the science community.  The term is very self-explanatory.

At the time I write this, Fall has just arrived and winter is around the corner.  The temperature is falling every day and it seems like there is a chill in the air every morning.  Sometimes when I wake up I don't want to get out of bed because of the cold chill in the room.  Just thinking of the term Absolute Zero sends a shiver down my spine.

So what does Absolute Zero mean?  Absolute Zero is a theoretical temperature at which the amount of thermodynamic energy in a system is at it's minimum.  Basically, it is as cold as it can get.

For the last few hundred years humans have been speculating what happens to matter as it approaches Absolute Zero.  Only in the last few decades have we had the technology to experiment at temperatures very close to absolute zero.  What we have found is that matter behaves very differently at these temperatures.  We are just now learning very little about what happens to atoms as we get temperatures close to Absolute Zero.  We still have a lot to discover.

To give you an idea of how cold Absolute Zero is, we need to look at what temperature scales are used.  In everyday life, we use Fahrenheit and Celsius to determine temperature.  When working with super cold temperatures, scientists prefer the Rankine and Kelvin Scales.  Absolute zero in both Rankine and Kelvin is set at 0 degrees.  To give you an idea of how cold that is, 0 degrees in Rankine is -459.67 degrees Fahrenheit and 0 degrees Kelvin is -237.15 degrees Celsius.   Brrrr...

In nature, the only place that gets cold enough to be close to Absolute Zero is outer space.  The average temperature in outer space is about 2.73 Kelvin.  Try using some of the calculators below to determine what that would temperature would convert to in Fahrenheit or Celsius.

So the next time you watch a science fiction movie, or see an astronaut in a picture, think about how thickly insulated that space suit has to be.  And this winter, be thankful that it's not THAT cold outside.

Try some of these online calculators to convert temperature.

Fahrenheit to Rankine Conversion Calculator

Rankine to Kelvin Conversion Calculator

Kelvin to Celsius Conversion Calculator

Kelvin to Rankine Conversion Calculator

Celsius to Kelvin Conversion Calculator

Other Online Calculators for Temperature Conversion.

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

Naturally, Math Is a Natural Occurrence in Nature

Nature is full of math.  To some, it may be very obvious, for others you may be oblivious to the fact that there is math in use all around us.  Many people think math is difficult, but I think that is in their head.  Every person processes math multiple times a day, and most likely they don't realize it.  Just look around and you will see math in nature, from small animals and plants, to weather and natural disasters.

When looking at plants and animals, one thing that comes to mind for me is a tree.  Sure, trees grow randomly and none are exactly the same, but one of the things I learned when I was young was that when a tree is cut down, you can determine the age of the tree by counting the rings on the stump.  There's some math.

How about clovers?  Have you ever heard of receiving luck if you find a four-leaf clover?  You can't get any luck with a three-leaf clover, you better be able to do some simple math for the difference.

Have you ever noticed that patterns emerge in mathematical practices?  They also emerge in nature.  Spider webs, bird migration, and even fish show patterns that can be described using mathematical concepts.

Probably the most obvious relation between math and nature is through weather and natural disasters.  Just turn on the news each morning and you'll hear math used in explaining weather.  They might report temperature, wind speed, percentages, rain fall, probabilities, it is all math.  And when it comes to natural disasters, just about every conceivable occurrence has a rating system that is derived from math.  For some examples; Tornadoes have the Fujita Scale, earthquakes have the Richter Scale and Hurricanes have a Category Scale.

So don't allow yourself to be challenged by math.  Math is one of the most natural thought processes to have.  Embrace mathematics as part of your lifestyle.

For more information on math in nature, particularly in regards to weather and natural disasters, try some of these online calculators.

Weather and Nature Calculators

Temperature Calculators

Earthquake Damage and Energy Calculator

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

Get Interested in Knowing More About Interest

Everyone should have an interest in learning more about interest.

That statement may sound a little silly, or redundant, but it is very true.  Interest is an aspect of finance that has become a major factor in how we live our lives.  Interest is basically a way for someone to earn money from loaning money.  It sounds confusing, but if you loan one penny to a friend, you no longer have the ability to use that penny for your own needs, and you have added a level of risk that you may not get that penny back.  To help offset the risk of never getting that penny back, and to help with the loss of you ability to use that penny if an opportunity comes up, you may want to charge a small fee.  This fee that a lender charges is called interest.

Interest is a fee that is set as a percentage rate per dollar borrowed.  This percentage can go up, or down, depending on a lot of factors.  Factors that can affect the rate are typically adjusted by the amount of risk that the loan may not be paid back, the amount of the loan, and the overall opinion on where else that money could be better used in a market.

My father always told me that there are two sides to interest.  There is a good side, and a bad side.  Of course, the bad side is when you pay interest to someone to borrow money from them.  Whether it be a car, house, credit card, or general loan, they have leverage over you to earn money from what you have borrowed.  The good side of the interest is to be the person loaning money and earning interest.  As someone who is loaning money, interest is a way to earn a profit and to reduce your risk of loaning the money out.

There has been much speculation in the recent years of predatory lending.  That is, groups that loan money at extremely high interest rates to people that need money and may not understand what they are agreeing to.  Educate yourself on interest, compound interest, and how it is calculated.

For more on interest and how it is applied in borrowing, or how interest can be earned, try using some of these online calculators.

Compound Interest Investment Calculator

Vehicle Loan Monthly Payment Calculator

Mortgage Loan Monthly Payment Calculator

Financial and Business Calculators

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

An Energetic Look at Temperature Measurements

When I think of temperature, I usually think of two things.  I think of temperature as it relates to weather and I think of temperature as it relates to my health.  I'm sure I'm not alone in those thoughts.  We look at temperature measurements everyday.  Anytime you turn on the TV or radio to find figure out how to dress appropriately, I would assume the air temperature has a big affect on your decision.  The importance of knowing what temperature is, what it measures, and how it affects us isn't limited to our daily fashion decisions.

First, what are we measuring when we measure temperature?  Temperature really is a measurement of energy.  Heat is a result of the amount of energy that is in the particles of a substance.  Does that make sense?  In other words, in a particular substance, like air, there are tiny particles that are moving and bouncing off each other.  The more energy that is in the substance, the more these particles move and bounce, giving off heat.  When you think of the term "cold" don't think of it as the opposite of heat, think of it as a lack of heat, or lack of energy in a substance.  A piece of ice has a lot less heat energy stored in the particles than boiling water does.  After all, to boil water, don't you add energy to it?

So, now that we barely scratched the surface of what temperature is measuring ( energy ), we can look at what methods are used to measure it.  In the U.S. we typically use Fahrenheit as the standard temperature measurement system.  We also use the Metric standard of Celsius, or Centigrade.  Most of the world uses the Metric standard.  In science, the use of Kelvin as a temperature standard is sometimes used, but is used typically for very cold measurements.

Sometimes, we will adjust our view of temperature from what the measurement actually is, to what it "feels" like.  When we use temperature to estimate our comfort level for outdoor activities, we often times will adjust for other factors that can affect how the temperature feels.  An example of one of these adjustments is the wind chill factor.  When the wind is blowing across our bodies, it can make the outside air temperature seem much cooler than the actual temperature.  In fact, the air movement helps to dissipate heat from our body, aiding in the cooling affect.  Another example on the opposite side of the spectrum is the heat index.  When there are high levels of moisture in the atmosphere the air surrounding our body isn't able to absorb as much of the heat energy within our bodies and we tend to feel warmer than the actual outdoor temperature readings may show.

It is important to know some of the math behind these temperature readings and how the wind chill and heat indices work.  For more information on how to convert temperatures and how we adjust these measurements to determine our comfort levels, try some of these online calculators.

Celsius to Fahrenheit Conversion Calculator

Fahrenheit to Celsius Conversion Calculator

Heat Index Calculator

Wind Chill Calculator

Temperature Calculator Menu

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

Time. The Most Important Measurement Since the Beginning of...Itself

Time is referred to so many times in a day.  Think about how many moments you take to look at a clock, a watch, or your cellphone.  We use time to judge where we are in our daily routine, or to coordinate a certain event.  But, we also use time as a measurement.  We think about how much time has lapsed from one event, to the next.

When looking at time as a comparing measurement between two events, rather than a reference to where we are in our daily routine, it is easy to look at sports as an example.  In most sports, there is an element of time.  You can have a set amount of time that you have to perform the best you can, such as the 4 quarters of a basketball game.  There can also be a measurement of time as a comparison of the sport.  In track, the competitor with the quickest time to run a set distance is the winner.

Because time is so important with our lives, it is important to be able to measure time and understand the math of time to accurately compare.  Luckily, time is not measured differently in Metric, or U.S. Standard measurements.

Over the centuries, our time units have been derived from how the Earth rotates and revolves around the sun.  This results in our seasons, years and days.  From there we break down our measurements further to hours, minutes, and seconds.

Sometimes it can get confusing if you are looking at other planets and how they are arranged around the Sun.  Because a year is how long it takes the Earth to revolve around the Sun, it does not work the same for other planets.  It takes much longer for some planets to make a full revolution around the sun, therefore one year for that planet would be multiple Earth years.  The same can be said for days.  One Earth day is how long it takes the Earth to turn one full rotation.  On other planets it may take longer to make a full rotation.  That planet's day, would be multiple Earth days.

Enough with some of the basics of time.  I could spend a lot of time discussing this.  It is important to know how to convert from years, to days, hours, minutes, and seconds.  For more on time and how to convert between these units, try using this online calculator:

Time Conversion Calculator

To see how time can be used in conjunction with other mathematical concepts like speed, flow rate, and navigation, browse through some of these other online calculators:  (But only if you have enough time)

Online Calculator Categories

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)