This web site allows users to evaluate expressions (including those which have variables – each with one or more values), and display the results in an easy-to-read table.  Many standard mathematical constants and functions are available for use in the expressions, as well as a collection of special purpose functions for a variety of computational chores (for example, calculating race pace, refinance and mortgage payoff strategies, performing integrations, calculating the number of calories burned by various workouts).  The button (above left) allows you to get more details about these and other capabilities, and the other buttons above (e.g., , , , ) lead to information which may be useful in building computations.  The button presents more detail about how to use this site effectively, the button brings up this page, and the button provides a mechanism for sending comments, questions and/or requests to us.

There are several advanced features, including storing results for later use, building user-defined functions, input shortcuts, and integration.  Click → for details.

The major capability is to evaluate expressions and equations (including those that have variables) and print the results out in a table for easy review.  Below are five samples:

1)	A simple equation with a constant, two functions, and two variables
2)	Calculate race times and race paces
3)	Calculate calories consumed during a bike ride and other actvities
4)	Investigate mortgage payoff strategies (various extra payments each month)
5)	Calculate the implications of refinancing a mortgage

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Sample 1)     tr = (pi-2.375)*(sqrt(x)*cos(omega-x))

Calculate values for tr for three values of x and three values of omega.  This is a two-step operation: first enter the equation into the [Expr] box (as in the sample below) and click .

Expr   tr = (pi - 2.375)*(sqrt(x)*cos(omega-x))

and second, enter value(s) for the variables (as in the sample below) and click .

x	5 7 10
omega	5.18, 9.1, 17.104

This will yield the results shown below:

tr = (PI-2.375)*(Sqrt(x)*Cos(omega-x));

		tr	x	omega
		------	---	---------
Max	1)	1.6864589	5	5.18
	2)	-0.9853364	5	9.1
	3)	1.534163	5	17.104
	4)	-0.500223	7	5.18
	5)	-1.0239357	7	9.1
Min	6)	-1.5780752	7	17.104
Mdn	7)	0.2603652	10	5.18
	8)	1.5068937	10	9.1
	9)	1.6523817	10	17.104

This sample illustrates the use of variables (x and omega), uses an equation (an equation is a result variable (tr), followed by "=" and an expression).  The nine result values of tr are automatically saved in the Store.  If you use tr in a subsequent computation during this session, those nine values will automatically be loaded (although you can edit or override them).  One constant (PI) and two functions – Sqrt() and Cos() – are also used.  The maximum, minimum and median value of the results are flagged.  Further, note that whitespace is ignored in the [Expr] box, but that whitespace is important for entering variable values.  Values are separated by any combination of one or more blanks and commas.

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Sample 2)     Using Race Functions

How long will it take to run a marathon at a steady pace of 7:15 per mile?

The Racetime() function has three arguments (distance, minutes, and seconds).  It shows the time to cover the distance at the input pace.  Enter the information into the [Expr] box and click .

Expr   racetime( marathon, 7, 15 )

which yields

Racetime(MARATHON, 7, 15);

The Marathon:  26.21875 mi at 7:15/mi (8.28 mph) =>  3:10:05

In this sample, marathon is a constant.  The Racepace() function performs the reverse operation – it takes 4 arguments (distance, hours, minutes, seconds) and reports overall pace for a given distance and time.  In this sample, the variable xmin is used to check out the paces for various overall times.

Expr   racepace( marathon, 3, xmin, 0 )

Enter value(s) for xmin and click .

xmin	0 10 20 30 40 50

which yields

	Dist (mi)	Time	Pace
The Marathon:	26.21875	3:00:00	6:52/mi	(8.74 mph)
The Marathon:	26.21875	3:10:00	7:15/mi	(8.28 mph)
The Marathon:	26.21875	3:20:00	7:38/mi	(7.87 mph)
The Marathon:	26.21875	3:30:00	8:01/mi	(7.49 mph)
The Marathon:	26.21875	3:40:00	8:23/mi	(7.15 mph)
The Marathon:	26.21875	3:50:00	8:46/mi	(6.84 mph)

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Sample 3)    Calories burned

How many calories do you burn in a 50 minute, 13½ mile bike ride if you weigh 165 pounds?

You can use the Calories() function.  Enter calories() in the [Expr] box and click to see the arguments.  This yields the following table, which shows that the Calories() function can be used with 40 different activities (for this sample, we choose cycling):

Function	Args	Results	Prototype/Description	Expr Use?
Calories	5	text	Calories( activity, weight, dist, min, sec ):  Approximate calories consumed by various activities.  Arguments as in the table below.  For example: "Calories( running, 165, 3.25, 25, 20 )" yields "408 calories -- Running (165 lbs, 3.25mi in 25:20 =>  7:48/mi = 7.70 mph)".  See also Fitness(), HeartRate(), Karvonen(), Points(), Bmi() activity   weight     dist    min    sec    |   ‡ Others Walking lbs miles min sec | Aerobicdance, Aerobicshi†, Aerobicslo†, Basketball, Running lbs miles min sec | Handball, Hockey, Iceskating, Judo, Karate, Lacrosse, Cycling lbs miles min sec | Pingpong, Racketball, Rollerblading, Rollerskating, Swimmingmy† lbs yards min sec | Rowing, Skiingcc†, Skiingdh†, Skiingwater, Swimmingfy† lbs yards min sec | Snowshoeing, Snowshoveling, Soccer, Squash, Swimmingmm† lbs meters min sec | Taichi, Tennisd†, Tenniss†, Volleyball, Swimmingfm† lbs meters min sec | Wateraerobics Skiprope lbs rpm min sec | † Swimming__; my=(male,yards), fy=(female,yards); Golfcarry lbs # holes min sec |       mm=(male,meters), fm=(female,meters); Golfwalk lbs # holes min sec | † Aerobics__;  lo=low-impact,  hi=high-impact Others ‡ lbs 0 min sec | † Skiing__;  cc=cross-country,  dh=downhill Stepcount lbs # steps 0 0 | † Tennis_;  d=doubles,  s=singles	No

Enter the argument values into the [Expr] box (as below) and click .

Expr   calories( cycling, 165, 13.5, 50, 0 )

which yields

Calories( CYCLING, 165, 13.5, 50, 0 );

517 calories -- Cycling (165 lbs,  13.5mi in 50:00  =>  3:42/mi = 16.20 mph)

In this sample, cycling is a constant.  Check the Prototype/Description table above for other activities which are supported by Calories(), for example, running, swimming, tennis, walking, aerobics, ....

Here are two more Calories() samples (running and walking).

Expr   calories( running, 175, 3, 22, 40 )

which yields

Calories( RUNNING, 175, 3, 22, 40 );

402 calories -- Running (175 lbs, 3mi in 22:40 => 7:33/mi = 7.94 mph)

Expr   calories( walking, 140, 3.8, 63, 0 )

which yields

Calories( WALKING, 140, 3.8, 63, 0 );

254 calories -- Walking (140 lbs, 3.8mi in 1:03:00 => 16:35/mi = 3.62 mph)

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Sample 4)     Paying off a loan early

Consider a mortgage at 6.55%, with payment of $1,331.76 per month, and an outstanding balance of $204,236.70 – what will be the impact of paying an extra $200 each month (assuming no prepayment penalties)?  What about other amounts?

You can use the Payoff2() function.  Enter payoff2() in the [Expr] box and click to see the arguments.  This yields

Function	Args	Results	Prototype/Description	Expr Use?
Payoff2	4	table	Payoff2( payment, rate, balance, extra ):  Show impact of extra amount submitted with each future mortgage payment when the loan is partly paid off:     payment  =  Monthly payment (principal + interest only: no escrow)     rate  =  Annual interest rate (percent - e.g., 5.85)     balance  =  Current balance (principal)     extra  =  Extra amount with each payment Same as PayoffExtra2().  See also Refinance(), Mortgage(), and the other Payoff*() functions.	No

Enter the information into the [Expr] box (as below) and click .

Expr   payoff2( 1331.76, 6.55, 204236.7, 200 );

which yields

Balance = $204,237 at 6.55% with monthly payments of $1,331.76
Total responsibility = 334 payments (333 * $1,331.76 + $447.13)
= $443,923  ($239,687 = 54.0% is interest)

An extra $200/month saves $77,785 (17.5%),  pays off loan 94 months early

	Standard	$200 extra
	---------------	--------------
Balance	$204,237	$204,237
Payment	$1,331.76	$1,531.76
Last payment	$447.13	$47.65
Months	334	240
Interest	$239,687	$161,902
% Interest	54.0%	44.2%
	---------------	--------------
Total	$443,923	$366,138
	---------------	--------------
Savings	—	$77,785

This computation is based only on principal and
interest, and assumes no prepayment penalty.
Escrow (taxes + insurance) is not part of the computation.

This shows a set of results for paying an extra $200.00 with each monthy payment.  The impacts are an overall savings of $77,785 (17.5%) and a reduction of almost eight years of payments.

To investigate the impact of other extra amounts per month, use various values for the extra variable.  Enter:

Expr   payoff2( 1331.76, 6.55, 204236.7, add );

Note the variable add – picking a set of values for add allows us to do a simple parameter study.  That is, we can easily see the results of various extra payment amounts.  Now click , then enter the additional amount(s) to pay for each month (values for add) and click to see the impact

              Enter value(s) for add

add	50, 100, 168.24, 200, 250, 300, 400, 500

which yields

Balance = $204,237 at 6.55% with monthly payments of $1,331.76
Total responsibility = 334 payments (333 * $1,331.76 + $447.13)
= $443,923  ($239,687 = 54.0% is interest)

Monthly	Monthly	/-------------- Saves ------------\			Final	Total		Total
Extra	Payment	$	%	Months	Payment	Interest		Payments
-----------	-------------	-----------------------------------------			------------	------------------------		--------------
0	$1,331.76	—			$447.13	$239,687	54.0%	$443,923
$50	$1,381.76	$26,619	6.0%	31	$12.80	$213,068	51.1%	$417,304
$100	$1,431.76	$47,323	10.7%	56	$3.15	$192,364	48.5%	$396,601
$168.24	$1,500	$69,318	15.6%	84	$1,105.15	$170,368	45.5%	$374,605
$200	$1,531.76	$77,785	17.5%	94	$47.65	$161,902	44.2%	$366,138
$250	$1,581.76	$89,408	20.1%	109	$201.20	$150,279	42.4%	$354,515
$300	$1,631.76	$99,364	22.4%	122	$257.47	$140,322	40.7%	$344,559
$400	$1,731.76	$115,583	26.0%	144	$1,037.17	$124,103	37.8%	$328,340
$500	$1,831.76	$128,280	28.9%	161	$580.17	$111,406	35.3%	$315,643

This computation is based only on principal and
interest, and assumes no prepayment penalty.
Escrow (taxes + insurance) is not part of the computation.

Note that the Payoff() function is similar to Payoff2(), except that Payoff() works with a loan starting at the beginning instead of during the payoff lifetime.  To see other financial functions, go to the top of this page and click   → ,   or click   → .  The financial function Refinance() is described below.

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Sample 5)     Refinancing a loan

Consider a mortgage at 7.375%, with payment of $1,885.66 per month and outstanding balance of $210,420 – what will be the implications of refinancing at 5.125% with a $2,750 refinance charge and taking out an additional $5,000 equity loan?

You can use the Refinance() function.  Enter refinance() in the [Expr] box and click to see the arguments.  This yields

Function	Args	Results	Prototype/Description	Expr Use?
Refinance	7	table	Refinance( currBalance, currPayment, currRate, newRate, loanCharge, loanLoan, newDuration ):  Impact (total cost, breakeven, % interest, et cetera) of refinancing a loan:     currBalance – Current loan balance (principal)     currPayment – Current loan payment (principal and interest components only)     currRate – Current loan annual interest rate (percent - e.g., 7.125)     newRate – New loan annual interest rate (percent - e.g., 5.75)     loanCharge – Addition to principal (loan charge - e.g., closing costs, points)     loanLoan – Addition to principal ("equity" payout - may be 0)     newDuration – New loan duration (years) Notes: (1) Do not include escrow payments (typically taxes and insurance) with currPayment,  (2) See also Mortgage() and the Payoff*() functions	No

The Refinance() function has 7 arguments.  Enter the information into the [Expr] box (as below) and click .

Expr   refinance( 210420, 1885.66, 7.375, 5.125, 2750, 5000, 15 );

which yields

Refinance(210420, 1885.66, 7.375, 5.125, 2750, 5000, 15);

Balance = $210,420.00 at 7.375% with monthly payments of $1,885.66
Current responsibility = 189 payments (188 * $1,885.66 + $1,809.77)
= $356,313.85  ($145,893.85 = 40.9% is interest)

	Current Mortgage	New Mortgage (w/out Equity)	New Mortgage (w/ Equity)	New Mortgage   (Old Payment)
	------------	---------------	---------------	----------------
Interest Rate	7.375%	5.125%	5.125%	5.125%
Equity "Loan"		0.00	$5,000.00	$5,000.00
Balance	$210,420.00	$213,170.00	$218,170.00	$218,170.00
Payment	$1,885.66	$1,699.65	$1,739.51	$1,885.66
Last Payment	$1,809.77	$1,699.65	$1,739.51	$1,710.84
Months	189	180	180	160
Breakeven		15	37	22
Interest	$145,893.85	$92,767.00	$94,941.80	$83,360.78
% Interest	40.9	30.3	30.8	28.1
	------------	---------------	---------------	----------------
Total To Pay	$356,313.85	$305,937.00	$308,111.80	$296,530.78
	------------	---------------	---------------	----------------
Savings	—	$50,376.85	$48,202.05	$59,783.06

This computation is based only on principal and
interest, and assumes no prepayment penalty.
Escrow (taxes + insurance) is not part of the computation.

• "Breakeven" is defined as the time (months) from the new mortgage til the current and new balances are the same.  This computation is more representative than the simpler (delta dollars)/(delta payment) method, and when the new interest rate is lower than the old rate, will result in a quicker breakeven.
  
  
• Note that the $5,000.00 equity "loan" with the refinance will end up costing $7,174.80 (that is, $2,174.80 in interest)
  
  
• The rightmost column represents the "what-if" computation of getting the new loan (5.125%), but continuing to pay it off with the old payment ($1,885.66)

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Click Advanced Features to review some of the more advanced ways to use ComputeSoup (also available via → ).

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