HECHT, Justice.

Several property owners sued the city of Indianola challenging the special assessments levied for paving a gravel road abutting their property and installing a sidewalk. The district court found the property owners had been assessed in excess of the special benefits received from the project and reduced the assessments. The city appealed. We affirm in part, reverse in part, and remand for further proceedings.

I. Factual and Procedural Background.

Plaintiffs own residential acreages along West Euclid Avenue on the west edge of the city of Indianola. West Euclid was a gravel road until the school board decided to build an elementary school along the avenue and the city council decided to pave it. The paving project included expanding and paving the avenue, reconfiguring ditches, and installing sidewalks on both sides. The city council's decision to pave was based on the location of the school, and none of the owners of the residential acreages had requested that the road be paved.

The paved road was thirty-one feet wide and eight inches thick. The city levied a total of $360,448.81 in special assessments for the pavement of the road and $41,080.32 for the installation of the sidewalk. The assessment district included the properties abutting West Euclid and back to a depth of 300 feet.1 The final assessments levied against the plaintiffs were as follows:

   Phillip and Linda Gray               $20,855.45
   Randall Ingram                       $11,697.64
   Loren Meyer and Linda Meints-Meyer   $16,694.32
   Lucille Sindric                      $16,694.32
   James and Tracy Steffen              $16,694.32
   Dennis and Mary Ripperger            $20,036.512

Several owners of property within the assessment district sued the city,3 contending the assessment exceeded the special benefits they received from the project. The various owners testified they did not receive much, if any, benefit from the paving of the road. They asserted they had purchased their property because they valued the rural atmosphere of which the gravel road was a feature. They believed their property values had decreased as a consequence of increased traffic prompted by the pavement of the road and the location of the school in the neighborhood. The owners opined access to their properties was not improved by the paving of the road. They also testified that the expected benefits of paving a gravel road, such as reduced noise and dust, were offset by the detriment resulting from the increased traffic due to the school. The owners also testified they did not believe the sidewalk benefitted their properties at all but actually constituted a detriment because they would now be required to maintain the sidewalks, including clearing snow in the winter. The owners further believe their exposure to liability for personal injuries to pedestrians increased as a consequence of the construction of the sidewalks which prompted an increase of pedestrian traffic. At least one owner purchased additional insurance to address his perception of this increased risk. Some owners conceded their properties might have more curb appeal because of the paved avenue, but none admitted any interest in selling their property.

The owners presented the expert testimony of Harold Smith, a former city engineer of the city of Des Moines. Smith opined that the method utilized by the city to spread part of the cost of the paving project among the abutting landowners, commonly called the Flint formula, was improper in this situation because the assessed properties are residential acreages. He testified that the city's use of the Flint formula, a purely mathematical formula based on frontage feet and distance from the improvements, resulted in excessive assessments. Smith criticized the city's application of the formula, asserting it failed to consider (1) the unique features of each parcel of land and (2) whether special benefits would actually be conferred to the properties burdened by the assessments.4 He proposed an alternate formulation of the assessments, multiplying the number of frontage feet of each parcel abutting the improvement by his calculation of the cost per foot of a twenty-five-foot wide, seven-inch thick road.5 He then considered fifteen "special benefit factors" to determine whether the paved street conferred special benefits upon the properties or general benefits to the city as a whole and concluded the paved road conferred little, if any, benefit upon the abutting landowners.6 Finally, after considering the unique features of each parcel, including whether it could be subdivided, his report concluded

The city presented evidence that while the Flint formula was utilized in part, the assessments in this case were not based entirely on a mechanical application of the Flint formula without consideration of the special benefits conferred upon the properties. Jeremy Enano, the engineer who prepared the plat and assessment schedule for the city, explained that, before the Flint formula was even applied to any of the project costs, the city had deducted the cost of paving the intersections and had only considered the cost of installing pavement seven inches thick, rather than the eight inches that was actually installed. The city had also not included the cost of installing sidewalks in the intersections in the sidewalk assessment. The city manager, Timothy Zisoff, testified the formula was adjusted for certain lots at the direction of the city council. Enano and Zisoff explained the adjustments:

Zisoff also testified that city council members inspected the properties and met with the owners to evaluate the special benefits received by the properties. He explained that the final assessments represented the cost of installing a twenty-five-foot wide, seven-inch thick road, even though the road was wider and thicker.

In addition, the city presented evidence explaining that the Flint formula has for decades been the preferred and established method of calculating special assessments in Iowa. Smith, the owners' expert, conceded that the Flint formula, in various forms, is the most common method used by cities and engineers in the state, and he admitted it was the method he utilized during his tenure as city engineer of Des Moines. The city's experts testified the Flint formula is commonly used by municipalities to allocate assessments whether the property is residential or commercial.

The city's expert, Duane Wittstock, had been the city engineer for the city of West Des Moines since 1988. He testified that the Flint formula was applied appropriately in this case, citing the fact that the properties are fairly uniform in shape as an important consideration. He also identified a list of twenty special benefits the properties were likely to receive.7

The district court concluded that the assessments were excessive and reduced them, relying on Smith's testimony. The district court determined the general benefit derived from paving the road was greater than the special benefit accruing to the abutting property owners. The court reasoned that because the lots at issue extend beyond 300 feet from the road, the application of the Flint formula amounted to nothing more than an inappropriate frontage-foot method, which has been disapproved by our caselaw. Concluding the city did not take other factors into consideration but rendered the assessments based solely on the Flint method, the district court found the assessments excessive and reduced them. The district court relied on Smith's report and determined that the assessments may not exceed $8,453.788 and reduced the sidewalk assessments by half. The city appealed.

II. Scope and Standards of Review.

Our review is de novo. Horak Prairie Farm, L.P. v. City of Cedar Rapids, 748 N.W.2d 504, 506 (Iowa 2008). We will give weight to, but we are not bound by, the district court's findings. Id. On appeal, as in the district court, the burden is on the plaintiffs to show that the special assessments were excessive. Mulford v. City of Iowa Falls, 221 N.W.2d 261, 268 (Iowa 1974). Once the city has "properly ordered a special improvement . . . there is a presumption of necessity and a presumption, too, that some benefit results to the assessed property owners." Goodell v. City of Clinton, 193 N.W.2d 91, 93 (Iowa 1971). Further, there is a presumption that the assessments are correct and do not exceed the special benefit received from the improvement. Id. It is appropriate to consider "future uses and expectations as well as [the] present use to which the property is put." Id. "Unfortunately, mathematical and analytical certainty is usually impossible in these cases, and thus, we must rely on approximations to determine the correct amount of the assessment." Horak Prairie Farm, 748 N.W.2d at 508.

III. Discussion.

Iowa Code section 384.61 (2007) addresses the assessment of costs incurred by municipalities in the development of public improvements.

Iowa Code § 384.61. A special assessment cannot exceed twenty-five percent of the value of the property. Id. § 384.62(1). The statutory scheme provides limitations to "ensure that individual property owners are not subsidizing the general benefits enjoyed by the public resulting from the improvements, particularly when street improvements are at issue." Horak Prairie Farm, 748 N.W.2d at 507. In this case, the controversy centers on whether the property owners were assessed in excess of the special benefits they receive from the improvement. Specifically, the plaintiffs contend the city inappropriately relied on a purely mathematical formula, the Flint formula, to spread the costs of the street paving project among the abutting landowners resulting in assessments which are higher than the special benefit conferred upon their properties. The owners contend the city should have engaged in an individualized assessment of each parcel to gauge the benefits conferred upon the property.

The city does not dispute that it applied the Flint formula to spread the cost of the assessment to the properties; however, it contends the application of the formula was not inappropriate for two reasons. First, the city argues the assessments did not exceed the special benefits conferred upon the properties. Additionally, the city argues it did not merely apply a mathematical formula to calculate the assessments but instead used the formula as part of its individualized assessment of the benefits conferred upon the properties. The city requests we make clear that the use of the Flint formula is not proscribed by law, as the formula is currently being used in the vast majority of jurisdictions in the state.

A. Special Benefits Conferred upon the Properties. Upon our review of the record, we are not persuaded the plaintiffs have met their burden of establishing their assessments exceed the special benefits conferred on their properties as a consequence of the improvements on and along West Euclid. We have no doubt the city's primary purpose in undertaking this improvement project was the achievement of a public benefit after an elementary school was built in the neighborhood. West Euclid was widened and paved to accommodate the traffic to the school and connect other paved roads in the city to a relatively new housing development situated to the north of the plaintiffs' properties and accessible only via West Euclid. The development of a paved surface on the roadway conferred a broader public benefit as well because commuters use the improved road to connect to highways leading to Des Moines. The substantial benefits derived by the general public from the West Euclid paving project do not render the special assessment excessive, however, as the city did not assess the full cost of the project against the properties within the assessment district. Instead, at several points in the assessment process, the city reduced the assessment against the private landowners to balance the general benefits conferred upon the public with the special benefits conferred upon the abutting properties.

Initially, the city determined not to assess the cost of paving intersections against the abutting landowners. The city also decided to only assess for the cost of a seven-inch thick pavement, even though the road was eight inches thick. Of the cost remaining for the improvement of the road, $660,448.81, the city assessed $360,448.81,9 or approximately fifty-five percent, against the abutting landowners. Further, as we have already noted, when the Flint formula was utilized to spread the fifty-five percent of the cost of the road among the properties benefitted, the city directed the engineer to divide large lots and apply the formula to those lots in a way that would adjust the assessment for larger lots.

Few property owners are happy about sharing through special assessments the cost of public improvements, particularly ones that they did not ask for.

Chicago, R.I. & P. Ry. v. City of Centerville, 172 Iowa 444, 449, 153 N.W. 106, 108 (1915). One expects "property owners [to seek to] minimize the taxes they must pay for an improvement they did not want." Des Moines Union Ry. v. City of Des Moines, 459 N.W.2d 271, 273 (Iowa 1990).

According to the plaintiffs, virtually nothing about the paved road is better than the prior gravel road. One owner testified the pavement was worth one hundred dollars to him. Some of the plaintiffs testified the noise is louder and the dust is heavier than before the project was undertaken. They contend they have received little benefit in the way of improved access to their properties and that the road is not maintained better than before. The plaintiffs note increased vehicular traffic, more children and pedestrians, and the loss of the rural nature of their property as consequences of the project. Some of the owners admit that they will see slightly less wear on their cars because of the pavement and that there might be some improved curb appeal to a prospective buyer. Overall, however, they believe their property values have decreased since the road was paved.

We find the special benefits conferred upon the properties at issue in this case are numerous, despite the owners' testimony that they have actually been harmed by the paving of the road. Paving a gravel road confers substantial benefits on an abutting landowner, benefits that are "manifest to anyone having the slightest knowledge of the subject." Camp v. City of Davenport, 151 Iowa 33, 38, 130 N.W. 137, 139 (1911). The parties' experts identified many of them, including fugitive dust control, reduced roadway noise, lower vehicle maintenance costs, aesthetic enhancements, improved drainage, decreased potential for trash accumulation due to the elimination of ditches, increased safety, easier maintenance of the property abutting the road, and decreased response time for emergency services. Our review of the owners' testimony reveals that the heart of their complaint comes not from the improvement of the road but from the location of the school nearby, the increased traffic it has engendered, and the urban growth in the neighborhood.

Determining how much an improvement specially benefits abutting landowners rather than generally benefits others "cannot be done with mathematical precision. Approximation is the best we can do." City of Clive v. Iowa Concrete Block & Material Co., 298 N.W.2d 585, 592 (Iowa 1980) (citation omitted). We conclude the owners failed in this case to prove the assessments exceeded the special benefits conferred upon their properties, and the presumption that the assessments are correct has not been rebutted. Accordingly, we conclude the district court erred in setting aside the city council's assessments.

B. Use of the Flint Formula. The plaintiffs argue that while the Flint method may be appropriate in some situations, it should not be applied in the allocation of assessments to residential acreages. The plaintiffs contend the formula should not be used because it does not take into account variations in the assessed properties, such as topography, woods, ditches, and suitability for subdivision. Our caselaw has disapproved assessments calculated solely on area or frontage. See Wharton v. City of Oskaloosa, 158 N.W.2d 834, 835 (Iowa 1968) ("The area or frontage methods cannot be made the sole or conclusive basis of determining the assessments without regard to all other factors. . . ."); see also Des Moines Chrysler-Plymouth, Inc. v. City of Urbandale, 488 N.W.2d 711, 714 (Iowa Ct.App.1992). The use of a mathematical formula, however, as a tool in the principled allocation of assessments is not proscribed.10

Our cases have noted various factors relevant to the determination of the appropriate amount of special assessments, including the present and future use of the abutting property, the increase in the market value occasioned by the improvement, the size and shape of the property, the proximity of the property to the improvement, the amount of property fronting the improvement, the needs of the property owners served by the improvement, and the primary purpose behind the improvement. See Thorson, 531 N.W.2d at 650. The enterprise of quantifying and allocating special benefits conferred on affected properties is not an exact science.

In re Resurfacing Fourth St., 203 Iowa 298, 301, 211 N.W. 375, 377 (1926). We do not think the city's use of the Flint formula in this case was inconsistent with the applicable legal principles.

Furthermore, the challenged assessments were not based solely on the Flint formula. The city's council members viewed the properties at issue and discussed the proposed assessments with people in the neighborhood before the assessments were approved. At the direction of the city council, assessments of larger properties suitable for subdivision were adjusted in furtherance of the goal to quantify the special benefits derived by the respective properties. Under the circumstances of this case, we conclude the city's use of the Flint formula in the allocation of special assessments to benefitted properties was not improper.11

C. Sidewalk Assessments. Although an Indianola city ordinance requires property owners to install their own sidewalks, the city included the sidewalk installation as part of the West Euclid paving project and assessed the plaintiffs for the entire cost of the sidewalk fronting their properties. The district court concluded that because the city decided to install the sidewalks as part of the paving project and did not utilize a city ordinance compelling property owners to install their own sidewalks, the assessment for the sidewalk must not exceed the special benefits conferred upon the property as required by Iowa Code section 384.61. We agree that the special assessment levied against the properties for the installation of the sidewalk must not exceed the special benefit conferred upon the property. Brush v. Inc. Town of Liscomb, 202 Iowa 1155, 1158, 211 N.W. 856, 857 (1927) (holding special assessments levied for installation of sidewalk must not exceed special benefit conferred as required by statute even though city ordinance permitted assessment of full cost of sidewalk).

The property owners contend they suffered harm but derived no benefit from the installation of the sidewalk because they must now maintain the sidewalk and they are required to remove snow and ice from the walkways in the winter. They contend these new unsolicited responsibilities constitute a significant hardship, especially given the fact they will rarely use the sidewalks. The property owners also assert they now are burdened with unwelcome liability for injuries to pedestrians using the walkways. One property owner testified that he purchased additional insurance to cover this potential liability.

The record establishes the public benefit derived from the sidewalk improvements within the assessment district is significant. The city engineer testified the sidewalk was installed along West Euclid in furtherance of student safety, and the owners testified that students utilize the sidewalk to access the school. Sidewalks, particularly ones that connect with other sidewalks in the city, are used by the general walking public, just as streets are used by drivers. However, it is equally evident that sidewalks confer special benefits upon adjacent properties. Despite the protestations to the contrary, the plaintiffs in this case do receive special benefits from the sidewalk which will reduce the incidence of pedestrians walking through their property at other locations. Even the plaintiffs' expert conceded that an allocation of fifty percent of the cost of the construction of the sidewalk to the plaintiffs was appropriate. Like the district court, we find the assessment of the entire cost of the sidewalk improvements against the plaintiffs' properties cannot be sustained on this record because such an assessment would exceed the benefit conferred upon the adjacent properties.12 We affirm that portion of the district court's judgment reducing the sidewalk assessments by fifty percent.

IV. Conclusion.

We conclude the assessments levied by the city of Indianola against the plaintiffs for the road improvements did not exceed the special benefits conferred upon the plaintiffs' properties. We therefore reverse that part of the district court's judgment revising the assessments for the road improvements. However, we affirm that part of the district court's judgment reducing the special assessments against the plaintiffs' properties for the sidewalk improvements because the assessments failed to account for the significant public benefit occasioned by the sidewalks. Accordingly, we affirm in part, reverse in part, and remand for entry of a judgment consistent with this opinion.

AFFIRMED IN PART, REVERSED IN PART, AND CASE REMANDED.

All justices concur except APPEL, J., who takes no part.