Posts for Tag: calculator

Greenhouse gas emissions from airplane flights

Posted In: Environment | Transportation

Traveling by airplane produces significant greenhouse gas emissions

Flying in an airplane is likely the most greenhouse gas intensive activity you can do.  In a few short hours, you can can travel thousands of miles across the country or ocean.  It takes a large amount of fossil-fuel energy (oil) to lift an 80+ ton airplane off the ground and propel it at 600 miles per hour through the air.  Every hour of travel (in a Boeing 737) consumes around 750 gallons of jet fuel.

Even when dividing the fuel usage across all of the passengers (and cargo) of an aircraft, airplane travel consumes a significant amount of fuel per passenger.  The fuel economy is estimated to be about the same as a fairly efficient hybrid car driven by one person (60-70 passenger miles per gallon).  However, because you can go 10 times faster and much further more easily than you would in a car, airline travel can, on an absolute basis, emit larger amounts of greenhouse gases. In fact, an individual passenger’s share of emissions from a single airplane flight can exceed the annual average greenhouse gas emissions per capita from a number of countries (and the global average).

The following flight calculator and data visualization shows the miles and emissions produced per passenger by a airplane trip that you can specify.  Choose two airports that you are interested in and click the “Calculate Flight Emissions” button to see the emissions associated with a round-trip flight between these two cities.  The map will show you the flight route and also shows you the countries in the world where this one single round-trip flight produces more emissions per passenger than the average resident does in one year from all sources (annual per capita emissions).

In addition to individual countries, the tool also compares the flight’s per passenger emissions to the global average emissions per capita in 2017 (4.91 tonnes) and the emissions required to achieve a 22℃ climate stabilization in 2030 (3.08 tonnes) and in 2050 (1.37 tonnes). These 2030 and 2050 numbers are based on an International Energy Agency scenario.

Calculations of Airplane Emissions

The emissions calculated by this calculator are based on calculations from, a non-profit environmental organization.
The fuel consumption of a jet depends on the size of the aircraft and distance traveled, but takeoff and climbing to cruising altitude are particularly fuel-intensive. On shorter flights, the takeoff and initial climb will constitute a greater proportion of the total flight time so fuel consumption per mile will be higher than on longer (e.g. international) flights.

The detailed methodology is described in more detail in this document.

In addition to emissions of CO2 from the burning of jet fuel, jets also emit other gases (including methane, NOx, and water vapor) which can also contribute to warming (also known as “radiative forcing”). Because the emissions are occurring at high altitude, these gases can have different impacts than those at lower altitude. A number of studies have estimated the impact of these other gases can significantly contribute to the overall radiative forcing and have somewhere between 1.5 and 3 times the impact that the CO2 alone would. A number of studies, including the myclimate calculator use a factor of 2 to account for these non-CO2 gases and their warming impact, and that is what is used in this calculator as well.

Unlike cars, trucks and trains, it is much harder to power airplanes with batteries and electricity and producing low-carbon jet fuels from biomass is proving very challenging.

In order to achieve climate stabilization at 2 degrees C, global emissions need to basically go to zero over the next 40 years. With a growing global population, this means that the allowable emissions per person will shrink rapidly over these coming decades.

Ultimately, while aviation is a small part of global greenhouse gas emissions, it is a larger part of emissions in richer countries (i.e. if you are reading/viewing this post). And there are many in these richer countries who fly a disproportionate amount and therefore contribute a disproportionate amount of emissions. Hopefully, putting airplane travel in this context can help us better understand the impact of our actions and choices and maybe even change behavior for some.

Tools and Data Sources
The calculator estimates flight emissions based on the myclimate carbon footprint calculator. Data for CO2 emissions by country was downloaded from the European Commissions’s Emissions Database for Global Atmospheric Research. The map was built using the leaflet open-source mapping library in javascript.

airplane emissions

Visualizing the 4% Rule, Trinity Study and Safe Withdrawal Rates

Posted In: Financial Independence | Money

UPDATE: April 2020: I’ve updated the market data to include annual data up to and including 2019.
I also fixed a small bug which affected real stock market returns so you may see a very slight reduction in average returns and success rates.

Instructions for using the calculator:

This calculator is designed to let you learn as you play with it. Tweaking inputs and assumptions and hovering and clicking on results will help you to really gain a feel for how withdrawal rates and market returns affect your chance of retirement success (i.e. making it through without running out of money).

Inputs You Can Adjust:

  • Spending and initial balance – This will affect your withdrawal rate.  The withdrawal rate is really the only thing that is important (doubling spending and retirement savings will still yield the same success rate).
  • Asset allocation – Raise or lower your risk tolerance by holding more or less stock vs bonds
  • Adjust retirement length – This affects the number of historical cycles that are used in the simulation, but also increases risk of failure.
  • Add tax rates and investment fees – these will put a drag (i.e. lower) market returns and lower success rates

Options for Visualization:

  • Display all cycles – this is the mess of spaghetti like curves that show all historical cycle simulations
  • Display percentiles – this aggregates the simulations into percentiles to show most likely outcomes
  • Hover/Click on legend years – this will allow you to highlight a single historical cycle (you can also use the arrow keys to step through historical cycles)
  • Bottom graph can show either the sequence of returns (with average returns in 5 year periods) for a single historical cycle or distributions of returns in our historical data (1871 to 2016) and a single historical cycle.  You can choose to look at returns for stocks, bonds or your specific asset allocation.
  • The graph on the right shows a histogram of the ending balance of each historical cycle and color codes them to show percentiles.

What is the 4% Rule?

The 4% rule is a “rule of thumb” relating to safe retirement withdrawals.  It states that if 4% of your retirement savings can cover one years worth of retirement spending (an alternative way to phrase it is if you have saved up 25 times your annual retirement spending), you have a high likelihood of having enough money to last a 30+ year retirement. A key point is that the probabilities shown here are just historical frequencies and not a guarantee of the future. However, if your plan has a high success rate (95+%) in these simulations, this implies that retirement plan should be okay unless future returns are on par with some of the worst in history.

The overall goal of this rule and analysis is identifying a “safe withdrawal rate” or SWR for retirement.  A withdrawal rate is the percentage of your money that you withdraw from your retirement savings each year.  If you’ve saved up $1 million and withdraw $100,000 each year, that is a 10% withdrawal rate.

The “safe” part of the withdrawal rate relates to the fact that if your investments generally grow by more than your annual spending, then your retirement savings should last over the length of your retirement.  But average returns do not tell the whole story as the sequence of returns also plays a very important role, as will be discussed later.

One way to test this is through a backtesting simulation which forms the basis for the “Trinity Study”.

What is the Trinity Study?

The “Trinity Study” is a paper and analysis of this topic entitled “Retirement Spending: Choosing a Sustainable Withdrawal Rate,” by Philip L. Cooley, Carl M. Hubbard, and Daniel T. Walz, three professors at Trinity University. This study is a backtesting simulation that uses historical data to see if a retirement plan (i.e. a withdrawal rate) would have survived under past economic conditions.  The approach is to take a “historical cycle”, i.e. a series of years from the past and test your retirement plan and see if it runs out of money (“fails”) or not (“survives”).

How do you test withdrawal rate?

Given modern equity and bond market data only stretches back about 150 years, there is some, but not a huge amount of data to use in this simulation.  One example of a 30 year historical cycle would be 1900 to 1930, and another is 1970 to 2000.  The Trinity study and this calculator tests withdrawal rates against all historical periods from 1871 until the present (e.g. 1871 to 1901, 1872 to 1902, 1873 to 1903, . . . . 1986 to 2016).  Then across this 115 different historical cycles, it determines how many of these survived and how many failed.

The thinking is that if your retirement plan can survive periods that include recessions, depressions, world wars, and periods of high inflation, then perhaps it can survive the next 30-50 years.

The 4% rule that comes out of these studies basically states that a 4% withdrawal rate (e.g. $40,000 annual spending on a $1,000,000 retirement portfolio) will survive the vast majority of historical cycles (~96%).  If you raise your withdrawal rate, the rate of failure increases, while if you lower your withdrawal rate, your rate of failure decreases.

The goal of this tool is to help you understand the mechanics of the a historical cycle simulation like was used in the Trinity Study and how the 4% rule came to be. This understanding can help you better plan for retirement with the uncertainty that goes along with planning 30+ years into the future. If you want to also see how longevity and life expectancy play a role in retirement planning, you can take a look at the Rich, Broke and Dead calculator.

This post and tool is a work in progress. I have a number of ideas that I will implement and add to it to help improve the visualization and clarity of these concepts.

If 4% is a conservative rate, what is the maximum withdrawal rate?

The future is unlikely to be identical to any of the set of historical cycles that are used in this simulation. And yet, there are enough years of data that there are a fairly large set of possible outcomes from running a simulation with this input data. One way to understand this variation is to see in the main graph above that the ending balance can potentially vary by more than $5 million dollars on an inflation adjusted basis on a starting balance of $1 million.

Another way to see this same variation in market returns is by looking at maximum withdrawal rate. This is the highest amount that you could withdraw annually over your retirement and (just barely) not run out of money by the end of your retirement.

This graph shows the maximum withdrawal rate for a given historical cycle (i.e. 1871 to 1901). For example, in the 1871 to 1901 30 year historical cycle, you could have used an 8.8% withdrawal rate (inflation adjusted $80,000 withdrawal annually on a $1 million initial investment balance) and not run out of money. This is because the sequence of market (stock and bond) returns in this historical cycle were able to (barely) outpace the rate of withdrawals at the end of the 30 year retirement period. Many other cycles show lower successful withdrawal rates, because those cycles had poorer sequences of returns, while some had higher maximum withdrawal rates.
The graph also highlights those cycles that show a maximum withdrawal rate below 4% in red, while all others are shown in green. Most of these withdrawal rates are well over 4%, with some quite a bit higher. This again shows that if the future is somewhat like one of these historical cycles, most likely a 4% withdrawal rate will be enough for you to retire without running out of money and that it is likely that you could end up with more money than you started.

Data source and Tools Historical Stock/Bond and Inflation data comes from Prof. Robert Shiller. Javascript is used to create the interactive calculator tool and the create the code in the simulations to test each historical cycle and aggregate the results, and graphed using open-source, javascript graphing library.

4% rule trinity study

Visual Guide to Understanding Marginal Tax Rates

Posted In: Money

What is a marginal tax rate?

There is a fair amount of confusion about what a marginal tax rate is and how it affects how much tax you would owe the government on a certain amount of income. These graphs are here to help you better understand the difference between a marginal and average tax rate and to easily calculate these rates for specific examples in the US context. This tool only looks at US Federal Income taxes and ignores state, local and Social Security/Medicare taxes.

Marginal tax rates are the rate at which an additional dollar of income will be taxed at. There are different tax brackets (each with its own marginal rate) depending on which dollar of income you are looking at. This is very different from the Average (or effective) tax rate that is the result of applying these marginal tax rates across all of your income.

**Click Here to view other financial-related tools and data visualizations from engaging-data**

Instructions for using the visual tax calculator:

  • Select filing status: Single, Married Filing Jointly or Head of Household. For more info on these filing categories see the IRS website
  • Select percentage of regular income vs capital gains income. Regular income is wage or employment income and is taxed at a higher rate than capital gains income. Capital gains income is typically investment income from the sale of stocks or dividends and taxed at a lower rate than regular income.
  • Move your cursor or click on the graph to select a specific income Make sure you note that the x-axis is a logarithmic-scale, meaning that income grows exponentially as you move to the right.
  • Choose your graph preference One graph (Individual Tax Brackets) shows the individual tax brackets and how much of your income is taxed at the different marginal rates. The other graph (Aggregate Rates) shows the net result of applying the different rates to get your effective rate.
One of the most interesting things is to vary the proportion of regular income vs capital gains taxes. Generally, wealthier households earn a greater fraction of their income from capital gains and as a result of the lower tax rates on capital gains, these household pay a lower effective tax rate than those making an order of magnitude less in overall income.

Here are two tables that lists the marginal tax brackets in the United States in 2019 that form the basis of the calculations in the calculator. 2018’s numbers are pretty similar.

US Tax Brackets and Rates for 2019
Rate Single
Taxable Income Over
Married Filing Joint
Taxable Income Over
Heads of Households
Taxable Income Over
10% $0 $0 $0
12% $9,700 $19,400 $13,850
22% $39,475 $78,950 $52,850
24% $84,200 $168,400 $84,200
32% $160,725 $321,450 $160,700
35% $204,100 $408,200 $204,100
37% $510,300 $612,350 $510,300

You can see that tax rates are much lower for capital gains in the table below than for regular income (table above).

Capital Gains Brackets for 2019
Capital Gains Over
Married Filing Jointly
Capital Gains Over
Heads of Households
Capital Gains Over
0% $0 $0 $0
15% $39,375 $78,750 $52,750
20% $434,550 $488,850 $461,700

For those not visually inclined, here is a written description of how to apply marginal tax rates. The first thing to note is that the income shown here in the graphs is taxable income, which simply speaking is your gross income with deductions removed. The standard deduction for 2019 range from $12,200 for Single filers to $24,400 for Married filers.

  • If you are single, all of your regular taxable income between 0 and $9,700 is taxed at a 10% rate. This means that your all of your gross income below $12,200 is not taxed and your gross income between $12,200 and $21,900 is taxed at 10%.
  • If you have more income, you move up a marginal tax bracket. Any taxable income in excess of $9,700 but below $39,475 will be taxed at the 12% rate. It is important to note that not all of your income is taxed at the marginal rate, just the income between these amounts.
  • Income between $39,475 and $84,200 is taxed at 24% and so on until you have income over $510,300 and are in the 37% marginal tax rate . . .
  • Thus, different parts of your income are taxed at different rates and you can calculate an average or effective rate (which is shown in the aggregate rates graph).
  • Capital gains income complicates things slightly as it is taxed after regular income. Thus any amount of capital gains taxes you make are taxed at a rate that corresponds to starting after you regular income. If you made $100,000 in regular income, and only $100 in capital gains income, that $100 dollars would be taxed at the 15% rate and not at the 0% rate, because the $100,000 in regular income pushes you into the 2nd marginal tax bracket for capital gains (between $39,375 and $434,550).

Data and Tools:
Tax brackets and rates were obtained from the IRS website and calculations were made using javascript and plotted using the open source javascript plotting library.

marginal tax rates on regular and capital gains income

Age Calculator and Life Visualization

Posted In: Counting

This is a simple age calculator that calculates your age down to the second.

The age calculator should be relatively self-explanatory, just enter your birthdate into the tool.  You can also enter the time of birth (if you want to), otherwise it will assume you were born at midnight.

There are two options for viewing your “age”.

  • The first (“Numerical Age“) is a table that shows the number of years, months, days, hours, minutes and seconds since you were born. It also shows how long it will be until your next birthday.  You can also use the Start Clock button to see your age change each second.
  • The second (“Graphical age“) is a figure that shows your age in the context of a 90 year lifespan.  Each block shown is one week and there are 52 weeks (blocks) in a year (row) and 10 years (rows) per decade (group of blocks).

This visualization is based on the the very interesting Wait But Why post “Your Life in Weeks” by Tim Urban.  It’s a bit humbling to see your life laid out in this way, and to think about how you will spend the (hopefully many) remaining weeks of your life.

You can click the URL button to create a URL that is based on the your birthday (so you don’t have to type it in again).  Just copy the URL in the address bar at the top of your browser (after pressing the button) to share with others.

Programming: this program was written in javascript and uses the moment.js library to simplify the date calculations.

age calculator visualization

When Can I Retire? Early Retirement Calculator / FIRE Calculator

Posted In: Financial Independence | Money

UPDATE: April 2020: I’ve updated the market data to include annual data up to and including 2019.
I also fixed a small bug which affected real stock market returns so you may see a very slight reduction in real average returns and success rates.

How long do I need to save before I can retire?

This early retirement calculator / visualizer is designed to project the number of years until you can retire, based upon a few key inputs such as annual income and spending, income growth rate, expected annual spending in retirement and asset allocation. It is a pre-retirement calculator that is useful before you retire to get a sense of how many years it is likely to take to accumulate enough money to retire. The three primary modes that are available in the early retirement calculator are: (1) constant, single fixed-percentage real return rates, (2) historical series of real returns are applied to account for likely variability in future returns and (3) monte carlo simulation of the variable returns based upon user-specified input parameters.

This interactive calculator was built to let you play with the inputs and help you understand how savings rate and retirement spending strongly determine how long it will take you to save up for retirement. Note: it does not simulate the post-retirement period when you start to draw down your savings. That can be done on this post-retirement calculator (Rich, Broke or Dead) which compares the frequency of various outcomes in retirement (running out of money, ending up with way too much money, and life-expectancy).

Post-Retirement Calculator: Will My Money Survive Early Retirement? Visualizing Longevity Risk

Posted In: Financial Independence | Money

UPDATE: I’ve added two additional mortality tables for each sex, one representing a very healthy individual and thus longer expected lifespan, and one representing an unhealthy (smoker) individual with a shorter expected lifespan. This provides 3 different life expectancy curves (essentially low, average and high life expectancy). I also upgraded the spending flexibility parameter to allow you to determine at what percentage of your initial balance does the spending reduction kick in.

Rich, Broke or Dead?

One of the key issues with retiring is the question of outliving your money. This is also known as Longevity Risk and is especially important if you want to retire early, since your retirement could be 50 years long (or more). This interactive post-retirement calculation and visualization looks at the question of whether your retirement savings can last long enough to support your retirement spending and combines it with average US life expectancy values to get a fuller picture of the likelihood of running out of money before you die.

It helps to answer the question: If I start out with $X dollars at the beginning of my retirement, will I run out of money before I die?