# Turfgrass Mathematics Review/Practice Worksheet for Certified Turfgrass Professional Testing

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1 Turfgrass Mathematics Review/Practice Worksheet for Certified Turfgrass Professional Testing 1 MPH = 88 ft. / minute 5,280 ft. = 1 mile 43,560 ft 2 = 1 acre 27 ft 3 per yd M = 1 acre M = 1,000 ft fluid oz. = 1 gallon 4 quarts = 1 gallon GPM = gallons per minute GPA = gallons per acre N/M = nitrogen per 1,000 ft lb. = 454 grams 16 oz = 1 lb One acre inch of water = 27,154 gallons One acre inch of water = 3,630 cubic feet NOTE: Throughout this exercise M is used to represent 1,000 ft 2 Standard Fertilizer Calculations You want to apply 0.9 lb. N /M and you will use fertilizer. How much fertilizer per M? [ how much is the same as how many pounds] 0.9 lb. N /M = 3.6 lb fertilizer /M 0.25 How much fertilizer is needed per acre? 3.6 lb fertilizer /M * M/A = lb fertilizer per acre Need to spread 45 acres, how much fertilizer is needed? lb fertilizer per acre * 45 A = 7, lb fertilizer per 45 acres How many 50 lb bags are required for the 45 acres? 7, lb fertilizer per 45 acres = = 142 bags per 45 acres 50 lb /bag 1 P age

2 How many pounds of plant available N, P 2 O 5, & K 2 O (and elemental P and K) are in 1,250 lb of fertilizer? N P2O5 K2O 1,250 lb fertilizer * 0.05 = 62.5 lb of Nitrogen 1,250 lb fertilizer * 0.10 = lb of P 2 O 5 1,250 lb fertilizer * 0.20 = lb of K 2 O Sometimes it is useful/necessary to be able to convert P 2 O 5 and K 2 O to elemental P and K based on how soil test data might be reported. To convert P 2 O 5 to P, multiply by 0.44 (and vice versa, to convert P to P 2 O 5, divide by 0.44); to convert K 2 O to K, multiply by 0.83 (and divide by 0.83 to convert K to K 2 O). Using the values for P 2 O 5 and K 2 O from the previous problem, the pounds of P and K would be: P K lbs of P 2 O 5 * 0.44 = 55 lbs P (Note: 55 lbs P 0.44 = 125 lbs P 2 O 5 ) lbs of K 2 O * 0.83 = lbs K (Note: lbs K 0.83 = 250 lbs K 2 O) Practice problems: You want to apply 0.7 lb. N /M and you will use fertilizer. How much fertilizer per M? [ how much is the same as how many pounds] 4.37 lb fertilizer /M How much fertilizer is needed per acre? lb fertilizer per acre Need to spread 45 acres, how much fertilizer is needed? 8,575.9 lb fertilizer per 45 acres How many 50 lb bags are required for the 45 acres? 172 bags per 45 acres 2 P age

3 How many pounds of plant available N, P2O5, & K2O (and elemental P and K) are in 2,000 lb of fertilizer? N P2O5 K2O P K lb of Nitrogen 80.0 lb of P 2 O lb of K 2 O 35.2 lb P lb K If 1.2 lbs. of P2O5 per M is desired, how much of a fertilizer would be needed? 40.0 lb fertilizer /M How much of a fertilizer would be needed to supply 29.0 lb of nitrogen? lb fertilizer /M You want to put 0.90 lb N / M with a fertilizer over 65,000 ft 2. How much product is needed per M? 3.91 lb fertilizer /M For the whole area [65,000 ft 2 ]? lb fertilizer /65 M How much fertilizer will you need, to supply the annual requirement of 3 lbs. of N per 1,000 sq ft to 45,000 sq ft of greens? lb fertilizer /45 M 3 P age

4 Fertilizer Calculations Considering Nutrient Cost It also is sometimes quite useful to consider the costs of fertilizer sources based on the cost per pound of nutrient, quite often the price per pound of Nitrogen. KEY: REMEMBER YOU WANT TO FIND THE PRICE PER POUND OF N = \$ of bag Lb nitrogen in the bag Find the price of a pound of nitrogen from the following: A 50 lb bag of fertilizer costing \$39.95 Remember the formula \$39.95 is the cost of the bag XX lb nitrogen in the bag To find the amount of nutrient in a container you MULTIPLY the size of the container by the % of nutrient. 50 lb bag * 38% N === 50 lb * 0.38 = 19.0 lb nitrogen in the bag NOTE: In a 50 lb bag, the amount of nutrient will be ½ the number on the bag. Ex has 23 lb N has 6 lb N has 12.5 lb N SO: \$39.95 is the cost of the bag = \$2.10 per lb nitrogen 19.0 Lb nitrogen in the bag Now use this information to compare the cost per pound of nutrient (in this case N) from several fertilizers with different prices: at \$ per 50lb bag \$ = \$2.81 per lb nitrogen 50 lb * 0.16 = 8.0 lb N at \$ per 50 lb bag \$ = \$2.71 per lb nitrogen 50 lb * 0.21 = 10.5 lb N So the is a better deal for the nitrogen. THIS TECHNIQUE CAN COMPARE ANY SIZE CONTAINER AND ANY PRICE BECAUSE IT GIVES YOU THE COST OF A POUND OF NITROGEN FOR EACH at \$ per 50 lb bag \$ = \$1.40 per lb nitrogen 50 lb * 0.46 = 23.0 lb N at \$ per TON \$ = \$1.28 per lb nitrogen 2000 lb * 0.32 = lb N So the is a better deal for the nitrogen. 4 P age

5 Practice problems: at \$ per 50 lb bag = \$2.33 per lb nitrogen at \$ per 50 lb bag = \$2.28 per lb nitrogen at \$ per 36 lb bag = \$2.53 per lb nitrogen at \$ per 100 lb bag = \$3.00 per lb nitrogen at \$ per 50lb bag = \$4.90 per lb nitrogen at \$ per 1500 lb bag = \$2.32 per lb nitrogen 5 P age

6 Water/Irrigation Calculations Information for you to use: 1 acre inch = 27,154 gallons, One acre inch of water = 3,630 cubic feet cu ft = one gallon HINT: FOR ALL THE PROBLEMS, YOU NEED TO FIND THE NUMBER OF ACRE INCHES REQUIRED FIRST, then calculate time, and finally multiply the total acre inches by 27,154 to find the total gallons needed How many acre inches of water are required to supply 0.8 inches of water to 10 acres for 8 weeks? 0.8 inches of water * 10 acres = 8 acre inches 8 acre inches * 8 weeks = 64 acre inches are needed total How many gallons of water does 64 acre inches equal? 64 acre inches * 27,154 gallons per acre inch = 1,737,856 gallons How many gallons of water are needed to supply 0.75 acre inches of water to 5 acres for 10 weeks? 0.7 acre inch * 5 Acres * 10 weeks = 37.5 acre inches total FIND THE TOTAL ACRE INCHES REQUIRED FIRST 37.5 acre inches * 27,154 gallons = 1,018,275 gallons total The irrigation system will spray 1.20 acre inch of water per week for 7 months over 25 acres. How many gallons will this be? 1.20 acre inch * 25 Acres = 30 acre inches 30 acre inches * (7 months * 4weeks/month) = 30 * 28 = 840 acre inches total 840 acre inches * 27,154 gallons = 22,809,360 gallons total How many cubic feet of dirt must be dug for the pond to contain the water needed to hold 22,809,360 gallons? 22,809,360 gallons are needed for the pond * cu ft/gallon = 3,056, ft 3 [cubic feet] How many cubic yards is this? [27 cubic feet = a cubic yard] 3,056, ft 3 = 113,202 yd 3 [cubic yards] 27 ft 3 /yd 3 6 P age

7 Practice problems: HINT: FOR ALL THE PROBLEMS, YOU NEED TO FIND THE NUMBER OF ACRE INCHES REQUIRED FIRST, Then calculate time, finally multiply the total acre inches by 27,154 to find the total gallons needed How many acre inches of water are required to supply 1.1 inches of water to 10 acres for 7 weeks? How many gallons does the answer above equal? 77 acre inches are needed total 2,090,858 gallons How many gallons of water are needed to supply 0.6 acre inches of water to 15 acres for 8 weeks? 1,955,088 gallons total How many cubic feet of dirt must be dug for the pond to contain 4,500,00 gallons 603,000 ft 3 [cubic feet] How many cubic yards is this? [27 cubic feet = a cubic yard] 22, yd 3 [cubic yards] If a 1000 gallon roadside sprayer sprays 20 gallons per acre and you are applying a product that requires 0.5 quarts of product per acre. Acres per tankload = 50 acres Product needed to cover a full tankload = 25 quarts If a 750 gallon fairway sprayer sprays 20 gallons of solution per acre and you are applying a product that requires 1.5 quarts per acre, how much product is needed to cover a full tankload? IN GALLONS gallons/ tankload 7 P age

8 Volumetric Calculations How much topdressing mix is needed to spread 1/8 inch over 5,000 sq ft? STEP #1 CONVERT THE THICKNESS INTO A DECIMAL [is still in inches, but now decimal form] 1/8 = inch STEP # 2 CHANGE THE INCHES INTO FEET BY DIVIDING BY 12 [12 inches per foot] inch / 12 in per foot = ft This gives you the thickness (height) in feet not inches. We are trying to find volume of material and volume is in cubic feet (ft 3 ). (Volume is surface area times thickness) STEP # 3 Multiply the area (ft2) times the thickness (in ft) equals volume (ft 3 ). 5,000 ft 2 times ft = ft 3 = the volume of material needed STEP # 4 If you want to find the amount of cubic yards of material needed. Divide by 27 [27 cubic ft in one cubic yd] ft 3 = cubic yards on topdressing needed 27 ft3/yd3 Now use 3/16 inch over 5,000 sq ft STEP #1 STEP #2 3/16 = inches thick divide by 12 = ft is thickness in feet STEP #3 Area * thickness = volume 5,000 ft 2 times ft = ft 3 STEP #4 Divide by 27 to get cubic yards ft 3 / 27 = yd 3 Practice problems: You will topdress 220,000 sq. ft. of greens with ¼ on material. How much material will be needed? Answer in cubic ft. and also cubic yards 4, ft yd 3 8 P age

9 How much material will be needed to topdress 125,000 sq. ft. of greens with 1/2 of material. Answer in cubic ft. and also cubic yards 5, ft yd 3 How much top dressing material is needed to cover 9,200 ft 2 green 5/16 inch deep answer in yd yd 3 How much mulch is needed to cover 1,200 ft 2 of area 3 inches deep answer in ft 3 Worked example: 3 /12 = 0.25ft 0.25 ft * 1,200 ft 2 = 300 ft 3 You will mulch 20,000 sq. ft. of flower beds with 3 of material. How much material will be needed? Answer in cubic ft. and also cubic yards 5,000.0 ft yd 3 9 P age

10 Calculations with Granular Pesticide Formulations Remember: 16 ounces = 1 pound [lb.] 1 pound = grams M = one acre Granular products = calculations are just like for fertilizers; AI (Active Ingredient) is a percentage of the weight] E.G. A formulation of 50 WP (wettable powder) = AI is 50%; common dry formulations are granular (G), dry flowables (DF), water dispersible granules (WDG). Granule (G) formulations are usually applied as is (granular form), while the other dry formulations are applied through a spray system with water as a carrier. Remember to find the amount of product, the math operation is division Team 2G = 2% ACTIVE INGREDIENT [ai] by weight. Want to spread 3 lb ai per A. How much product is needed? WANT = 3 lb /A = 150 lb product / A HAVE 0.02 Merit 0.5G = 0.5% ACTIVE INGREDIENT [ai]. An application rate is 0.4 lb ai per acre. How much product is needed? Important thing to remember: 0.5 % = WANT = 0.4 lb /A = 80 lb product / A HAVE Using Dacthal 75 WP at a rate of lb ai per acre, How much product is needed? Per Acre? = lb product / ai per acre Per 1,000 ft 2? = 0.31 lb / M Per 30,000 ft 2? = 9.41 lb / 30m = oz Remember to find the amount of AI, the math operation is multiplication -How much active ingredient is in a 50 lb bag of Drive 75 DF? Size of container * % ai = 50lb * 0.75 = 37.5 lb of AI 10 P age

11 You spread 600 lb of Team 2G over 3 acres. How much ai is applied per acre? 600 lb Team * 0.02 (2%) = 12 lb ai in the container divided by 3 acres = 4 lb ai per acre Practice problems: -How much active ingredient is in 80 lb of Sevin 10 G? = 8.0 lb of AI You spread 360 lb of Mach 1.5G over 3 acres. How much ai is applied per acre? = 1.8 lb ai per acre Use Sentinel 40 WG. The label says use 0.25 oz [of product] per 1,000 ft 2. How much ai is applied per acre? M = one acre Hint: = product oz / acre = 4.36 ai oz / acre 11 P age

12 Calculations with Liquid Formulations 128 fl oz = 1 gallon 1 ounce = 2 tablespoons 1 ounce = 29.6 milliliters The formulation number associated with liquid formulations of pesticides indicates the pounds of active ingredient [ai] per gallon Common liquid formulations are detailed on the label as liquid (L), emulsifiable concentrates (EC), microemulsions (ME), and suspension concentrates (SC). A 2.5 EC liquid has how much active ingredient PER GALLON? By definition it has 2.5 lb ai per gallon You want to apply 1.5 lb ai per acre of 2,4 D with a formulation of 4L to control weeds. How much product will you need for one acre? WANT = NEED 1.5 lb ai / A = 0.38 gallon / A * 128 fl oz / gallon = 48 fl oz/acre HAVE 4.0 lb ai / gallon You want to apply 0.75 pound AI per acre of Sabre Slime 3.5 L How many gallons of product are needed per acre? = gallons / acre How many ounces of product? = fl oz / acre If 3.0 gallons of a Wahoo Whiz 2.5 EC is applied to an acre. How much ai is put on an acre? 3.0 gallons * 2.5 lb ai /gallon = 7.5 lb ai per acre How much per 1,000ft 2 [M]? [43.56 M = one acre] 7.5 lb ai per acre / M/acre = 0.17lb ai / 1,000 ft 2 If you applied Betasan 4E at a rate of 8.8 fluid ounces [of product] per 1,000 ft 2. How much ai was applied per acre? Hint: How much product was applied per acre? Then determine the ai in that amount fl oz per acre = lb ai / acre You have 5 gallons of Great Stuff 6.0 EC. The directions say to apply 1.0 pound of AI per acre. How many acres can 5 gallons of product treat? Hint: how many lb of ai are in 5 gallons = 30 acres can be treated 12 P age

13 Pure Live Seed (PLS) Calculations Seeding rates for the various turfgrasses are on the basis of Pure Live Seed per unit area. This is important because seed purity and germination percentages vary depending on the variety/species of the grass selected and the seed source. The information you need to work with to determine Pure Live Seed is found on the seed tag. Pure live seed % s are calculated by multiplying the % purity and % germination for each variety in a seed blend or mixture. Each variety s % pure live seed values are calculated independently and then totaled for a %PLS value for the entire blend/mixture to use in determining how much seed product is required to deliver a targeted rate of pure live seed per unit area. For instance if a seed tag has the following information, one calculates the % PLS for each of the three varieties and totals these up to determine the %PLS for this blend of perennial ryegrasses. In this example, that is 74.1% PLS. Pure Seed Germination: 34.62% RunHard Perennial Ryegrass 80%.3462 *.80 = % KickFar Perennial Ryegrass 80%.3733 *.80 = % ThrowLong Perennial Ryegrass 75%.2197 *.75 =0.165 Other ingredients: = or 74.1% PLS 1.19% other crop seed; 4.89% Inert Matter If the goal is to apply 20 lbs of pure live perennial ryegrass seed per 1000 sq ft to a bermudagrass sports field (2.5 A), then the field manager would need 20 lbs product = 27 lbs of this product to deliver 20 lbs of pure live seed per 1000 sq ft. 2.5 A * 43,560 sq ft per A = 108,900 sq ft. 27 lbs : : x lbs = lbs of perennial ryegrass blend for the field 1000 sq ft 108,900 sq ft 13 P age

14 Practice problem: Pure Seed Germination: 33.34% Fiesta Perennial Ryegrass 85% = % Karma Perennial Ryegrass 83% = % Blazer Perennial Ryegrass 80% =0.259 Other ingredients: = 0.817% PLS 0.00% other crop seed; 1.11% Inert Matter If your goal is to apply 6 lbs of pure live perennial ryegrass seed per 1000 sq ft for a new homelawn establishment, how many pounds of this seed product would you need per 1000 sq ft of area? = 7.34 lbs If your lawn measures 12,500 sq feet, how many pounds of this seed blend are required to seed the entire lawn at 6 lbs of pure live seed per 1000 sq ft? = 91.8 lbs 14 P age

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